4z5+15+9=5z6-75

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.

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

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.

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.

Simplify the numerator.

Factor z out of 4z⋅6-5z⋅5.

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

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 -30⋅(-z30).

Cancel the common factor of 30.

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.

Multiply -1 by -1.

1⋅z=-30⋅(-535)

Multiply z by 1.

z=-30⋅(-535)

z=-30⋅(-535)

z=-30⋅(-535)

Simplify -30⋅(-535).

Cancel the common factor of 5.

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