Solve for y 7y^2=280-21y

Math
7y2=280-21y
Add 21y to both sides of the equation.
7y2+21y=280
Move 280 to the left side of the equation by subtracting it from both sides.
7y2+21y-280=0
Factor the left side of the equation.
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Factor 7 out of 7y2+21y-280.
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Factor 7 out of 7y2.
7(y2)+21y-280=0
Factor 7 out of 21y.
7(y2)+7(3y)-280=0
Factor 7 out of -280.
7y2+7(3y)+7⋅-40=0
Factor 7 out of 7y2+7(3y).
7(y2+3y)+7⋅-40=0
Factor 7 out of 7(y2+3y)+7⋅-40.
7(y2+3y-40)=0
7(y2+3y-40)=0
Factor.
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Factor y2+3y-40 using the AC method.
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Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -40 and whose sum is 3.
-5,8
Write the factored form using these integers.
7((y-5)(y+8))=0
7((y-5)(y+8))=0
Remove unnecessary parentheses.
7(y-5)(y+8)=0
7(y-5)(y+8)=0
7(y-5)(y+8)=0
Divide each term by 7 and simplify.
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Divide each term in 7(y-5)(y+8)=0 by 7.
7(y-5)(y+8)7=07
Simplify 7(y-5)(y+8)7.
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Cancel the common factor of 7.
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Cancel the common factor.
7(y-5)(y+8)7=07
Divide (y-5)(y+8) by 1.
(y-5)(y+8)=07
(y-5)(y+8)=07
Expand (y-5)(y+8) using the FOIL Method.
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Apply the distributive property.
y(y+8)-5(y+8)=07
Apply the distributive property.
y⋅y+y⋅8-5(y+8)=07
Apply the distributive property.
y⋅y+y⋅8-5y-5⋅8=07
y⋅y+y⋅8-5y-5⋅8=07
Simplify and combine like terms.
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Simplify each term.
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Multiply y by y.
y2+y⋅8-5y-5⋅8=07
Move 8 to the left of y.
y2+8⋅y-5y-5⋅8=07
Multiply -5 by 8.
y2+8y-5y-40=07
y2+8y-5y-40=07
Subtract 5y from 8y.
y2+3y-40=07
y2+3y-40=07
y2+3y-40=07
Divide 0 by 7.
y2+3y-40=0
y2+3y-40=0
Factor y2+3y-40 using the AC method.
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Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is -40 and whose sum is 3.
-5,8
Write the factored form using these integers.
(y-5)(y+8)=0
(y-5)(y+8)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
y-5=0
y+8=0
Set the first factor equal to 0 and solve.
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Set the first factor equal to 0.
y-5=0
Add 5 to both sides of the equation.
y=5
y=5
Set the next factor equal to 0 and solve.
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Set the next factor equal to 0.
y+8=0
Subtract 8 from both sides of the equation.
y=-8
y=-8
The final solution is all the values that make (y-5)(y+8)=0 true.
y=5,-8
Solve for y 7y^2=280-21y

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