# Solve for z 5/(5z+7)=1/(8z) 55z+7=18z
Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.
5⋅(8z)=(5z+7)⋅1
Solve the equation for z.
Multiply 8 by 5.
40z=(5z+7)⋅1
Multiply 5z+7 by 1.
40z=5z+7
Move all terms containing z to the left side of the equation.
Subtract 5z from both sides of the equation.
40z-5z=7
Subtract 5z from 40z.
35z=7
35z=7
Divide each term by 35 and simplify.
Divide each term in 35z=7 by 35.
35z35=735
Cancel the common factor of 35.
Cancel the common factor.
35z35=735
Divide z by 1.
z=735
z=735
Cancel the common factor of 7 and 35.
Factor 7 out of 7.
z=7(1)35
Cancel the common factors.
Factor 7 out of 35.
z=7⋅17⋅5
Cancel the common factor.
z=7⋅17⋅5
Rewrite the expression.
z=15
z=15
z=15
z=15
z=15
The result can be shown in multiple forms.
Exact Form:
z=15
Decimal Form:
z=0.2
Solve for z 5/(5z+7)=1/(8z)

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