z^2-9z=72-8z

Solution for z^2-9z=72-8z equation:

Simplifying
z2 + -9z = 72 + -8z

Reorder the terms:
-9z + z2 = 72 + -8z

Solving
-9z + z2 = 72 + -8z

Solving for variable 'z'.

Reorder the terms:
-72 + -9z + 8z + z2 = 72 + -8z + -72 + 8z

Combine like terms: -9z + 8z = -1z
-72 + -1z + z2 = 72 + -8z + -72 + 8z

Reorder the terms:
-72 + -1z + z2 = 72 + -72 + -8z + 8z

Combine like terms: 72 + -72 = 0
-72 + -1z + z2 = 0 + -8z + 8z
-72 + -1z + z2 = -8z + 8z

Combine like terms: -8z + 8z = 0
-72 + -1z + z2 = 0

Factor a trinomial.
(-8 + -1z)(9 + -1z) = 0

Subproblem 1
Set the factor '(-8 + -1z)' equal to zero and attempt to solve:

Simplifying
-8 + -1z = 0

Solving
-8 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '8' to each side of the equation.
-8 + 8 + -1z = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1z = 0 + 8
-1z = 0 + 8

Combine like terms: 0 + 8 = 8
-1z = 8

Divide each side by '-1'.
z = -8

Simplifying
z = -8
Subproblem 2
Set the factor '(9 + -1z)' equal to zero and attempt to solve:

Simplifying
9 + -1z = 0

Solving
9 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + -1z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1z = 0 + -9
-1z = 0 + -9

Combine like terms: 0 + -9 = -9
-1z = -9

Divide each side by '-1'.
z = 9

Simplifying
z = 9
Solution
z = {-8, 9}