Solve for z (4z)/5+1/5+9=(5z)/6-7/5

Math
4z5+15+9=5z6-75
Simplify 4z5+15+9.
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To write 9 as a fraction with a common denominator, multiply by 55.
4z5+15+9⋅55=5z6-75
Combine 9 and 55.
4z5+15+9⋅55=5z6-75
Combine the numerators over the common denominator.
4z5+1+9⋅55=5z6-75
Simplify the numerator.
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Multiply 9 by 5.
4z5+1+455=5z6-75
Add 1 and 45.
4z5+465=5z6-75
4z5+465=5z6-75
4z5+465=5z6-75
Move all terms containing z to the left side of the equation.
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Subtract 5z6 from both sides of the equation.
4z5+465-5z6=-75
To write 4z5 as a fraction with a common denominator, multiply by 66.
4z5⋅66-5z6+465=-75
To write -5z6 as a fraction with a common denominator, multiply by 55.
4z5⋅66-5z6⋅55+465=-75
Write each expression with a common denominator of 30, by multiplying each by an appropriate factor of 1.
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Multiply 4z5 and 66.
4z⋅65⋅6-5z6⋅55+465=-75
Multiply 5 by 6.
4z⋅630-5z6⋅55+465=-75
Multiply 5z6 and 55.
4z⋅630-5z⋅56⋅5+465=-75
Multiply 6 by 5.
4z⋅630-5z⋅530+465=-75
4z⋅630-5z⋅530+465=-75
Combine the numerators over the common denominator.
4z⋅6-5z⋅530+465=-75
Simplify each term.
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Simplify the numerator.
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Factor z out of 4z⋅6-5z⋅5.
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Factor z out of 4z⋅6.
z(4⋅6)-5z⋅530+465=-75
Factor z out of -5z⋅5.
z(4⋅6)+z(-5⋅5)30+465=-75
Factor z out of z(4⋅6)+z(-5⋅5).
z(4⋅6-5⋅5)30+465=-75
z(4⋅6-5⋅5)30+465=-75
Multiply 4 by 6.
z(24-5⋅5)30+465=-75
Multiply -5 by 5.
z(24-25)30+465=-75
Subtract 25 from 24.
z⋅-130+465=-75
z⋅-130+465=-75
Move -1 to the left of z.
-1⋅z30+465=-75
Move the negative in front of the fraction.
-z30+465=-75
-z30+465=-75
-z30+465=-75
Move all terms not containing z to the right side of the equation.
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Subtract 465 from both sides of the equation.
-z30=-75-465
Combine the numerators over the common denominator.
-z30=-7-465
Subtract 46 from -7.
-z30=-535
Move the negative in front of the fraction.
-z30=-535
-z30=-535
Multiply both sides of the equation by -30.
-30⋅(-z30)=-30⋅(-535)
Simplify both sides of the equation.
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Simplify -30⋅(-z30).
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Cancel the common factor of 30.
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Move the leading negative in -z30 into the numerator.
-30⋅-z30=-30⋅(-535)
Factor 30 out of -30.
30(-1)⋅-z30=-30⋅(-535)
Cancel the common factor.
30⋅-1⋅-z30=-30⋅(-535)
Rewrite the expression.
-1⋅(-z)=-30⋅(-535)
-1⋅(-z)=-30⋅(-535)
Multiply.
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Multiply -1 by -1.
1⋅z=-30⋅(-535)
Multiply z by 1.
z=-30⋅(-535)
z=-30⋅(-535)
z=-30⋅(-535)
Simplify -30⋅(-535).
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Cancel the common factor of 5.
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Move the leading negative in -535 into the numerator.
z=-30⋅-535
Factor 5 out of -30.
z=5(-6)⋅-535
Cancel the common factor.
z=5⋅-6⋅-535
Rewrite the expression.
z=-6⋅-53
z=-6⋅-53
Multiply -6 by -53.
z=318
z=318
z=318
Solve for z (4z)/5+1/5+9=(5z)/6-7/5

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