Solve for Q -5=(Q-20)/-400*5800/((Q+20)/2)

Math
-5=Q-20-400⋅5800Q+202
Rewrite the equation as Q-20-400⋅5800Q+202=-5.
Q-20-400⋅5800Q+202=-5
Factor each term.
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Multiply Q-20-400 and 5800Q+202.
(Q-20)⋅5800-400Q+202=-5
Reduce the expression (Q-20)⋅5800-400Q+202 by cancelling the common factors.
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Factor 200 out of (Q-20)⋅5800.
200((Q-20)⋅29)-400Q+202=-5
Factor 200 out of -400Q+202.
200((Q-20)⋅29)200(-2Q+202)=-5
Cancel the common factor.
200((Q-20)⋅29)200(-2Q+202)=-5
Rewrite the expression.
(Q-20)⋅29-2Q+202=-5
(Q-20)⋅29-2Q+202=-5
Combine -2 and Q+202.
(Q-20)⋅29-2(Q+20)2=-5
(Q-20)⋅29-2(Q+20)2=-5
Solve for Q.
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Multiply each term by -2(Q+20)2 and simplify.
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Multiply each term in (Q-20)⋅29-2(Q+20)2=-5 by -2(Q+20)2.
(Q-20)⋅29-2(Q+20)2⋅(-2(Q+20)2)=-5⋅-2(Q+20)2
Simplify (Q-20)⋅29-2(Q+20)2⋅(-2(Q+20)2).
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Reduce the expression by cancelling the common factors.
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Reduce the expression -2(Q+20)2 by cancelling the common factors.
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Factor 2 out of -2(Q+20).
(Q-20)⋅292(-(Q+20))2⋅-2(Q+20)2=-5⋅-2(Q+20)2
Factor 2 out of 2.
(Q-20)⋅292(-(Q+20))2(1)⋅-2(Q+20)2=-5⋅-2(Q+20)2
Cancel the common factor.
(Q-20)⋅292(-(Q+20))2⋅1⋅-2(Q+20)2=-5⋅-2(Q+20)2
Rewrite the expression.
(Q-20)⋅29-(Q+20)1⋅-2(Q+20)2=-5⋅-2(Q+20)2
(Q-20)⋅29-(Q+20)1⋅-2(Q+20)2=-5⋅-2(Q+20)2
Divide -(Q+20) by 1.
(Q-20)⋅29-(Q+20)⋅-2(Q+20)2=-5⋅-2(Q+20)2
(Q-20)⋅29-(Q+20)⋅-2(Q+20)2=-5⋅-2(Q+20)2
Cancel the common factor of Q+20.
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Factor Q+20 out of -(Q+20).
(Q-20)⋅29(Q+20)⋅-1⋅-2(Q+20)2=-5⋅-2(Q+20)2
Factor Q+20 out of -2(Q+20).
(Q-20)⋅29(Q+20)⋅-1⋅(Q+20)⋅-22=-5⋅-2(Q+20)2
Cancel the common factor.
(Q-20)⋅29(Q+20)⋅-1⋅(Q+20)⋅-22=-5⋅-2(Q+20)2
Rewrite the expression.
(Q-20)⋅29-1⋅-22=-5⋅-2(Q+20)2
(Q-20)⋅29-1⋅-22=-5⋅-2(Q+20)2
Multiply (Q-20)⋅29-1 and -22.
(Q-20)⋅29⋅-2-1⋅2=-5⋅-2(Q+20)2
Multiply.
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Multiply -2 by 29.
(Q-20)⋅-58-1⋅2=-5⋅-2(Q+20)2
Multiply -1 by 2.
(Q-20)⋅-58-2=-5⋅-2(Q+20)2
(Q-20)⋅-58-2=-5⋅-2(Q+20)2
Cancel the common factor of -58 and -2.
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Factor -2 out of (Q-20)⋅-58.
-2((Q-20)⋅29)-2=-5⋅-2(Q+20)2
Cancel the common factors.
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Factor -2 out of -2.
-2((Q-20)⋅29)-2(1)=-5⋅-2(Q+20)2
Cancel the common factor.
-2((Q-20)⋅29)-2⋅1=-5⋅-2(Q+20)2
Rewrite the expression.
(Q-20)⋅291=-5⋅-2(Q+20)2
Divide (Q-20)⋅29 by 1.
(Q-20)⋅29=-5⋅-2(Q+20)2
(Q-20)⋅29=-5⋅-2(Q+20)2
(Q-20)⋅29=-5⋅-2(Q+20)2
Apply the distributive property.
Q⋅29-20⋅29=-5⋅-2(Q+20)2
Simplify the expression.
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Move 29 to the left of Q.
29⋅Q-20⋅29=-5⋅-2(Q+20)2
Multiply -20 by 29.
29Q-580=-5⋅-2(Q+20)2
29Q-580=-5⋅-2(Q+20)2
29Q-580=-5⋅-2(Q+20)2
Simplify -5⋅-2(Q+20)2.
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Cancel the common factor of -2 and 2.
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Factor 2 out of -2(Q+20).
29Q-580=-5⋅2(-(Q+20))2
Cancel the common factors.
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Factor 2 out of 2.
29Q-580=-5⋅2(-(Q+20))2(1)
Cancel the common factor.
29Q-580=-5⋅2(-(Q+20))2⋅1
Rewrite the expression.
29Q-580=-5⋅-(Q+20)1
Divide -(Q+20) by 1.
29Q-580=-5⋅(-(Q+20))
29Q-580=-5⋅(-(Q+20))
29Q-580=-5⋅(-(Q+20))
Apply the distributive property.
29Q-580=-5⋅(-Q-1⋅20)
Multiply -1 by 20.
29Q-580=-5⋅(-Q-20)
Apply the distributive property.
29Q-580=-5(-Q)-5⋅-20
Multiply.
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Multiply -1 by -5.
29Q-580=5Q-5⋅-20
Multiply -5 by -20.
29Q-580=5Q+100
29Q-580=5Q+100
29Q-580=5Q+100
29Q-580=5Q+100
Move all terms containing Q to the left side of the equation.
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Subtract 5Q from both sides of the equation.
29Q-580-5Q=100
Subtract 5Q from 29Q.
24Q-580=100
24Q-580=100
Move all terms not containing Q to the right side of the equation.
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Add 580 to both sides of the equation.
24Q=100+580
Add 100 and 580.
24Q=680
24Q=680
Divide each term by 24 and simplify.
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Divide each term in 24Q=680 by 24.
24Q24=68024
Cancel the common factor of 24.
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Cancel the common factor.
24Q24=68024
Divide Q by 1.
Q=68024
Q=68024
Cancel the common factor of 680 and 24.
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Factor 8 out of 680.
Q=8(85)24
Cancel the common factors.
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Factor 8 out of 24.
Q=8⋅858⋅3
Cancel the common factor.
Q=8⋅858⋅3
Rewrite the expression.
Q=853
Q=853
Q=853
Q=853
Q=853
The result can be shown in multiple forms.
Exact Form:
Q=853
Decimal Form:
Q=28.3‾
Mixed Number Form:
Q=2813
Solve for Q -5=(Q-20)/-400*5800/((Q+20)/2)

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