z^2+8z=128

Solution for z^2+8z=128 equation:

Simplifying
z2 + 8z = 128

Reorder the terms:
8z + z2 = 128

Solving
8z + z2 = 128

Solving for variable 'z'.

Reorder the terms:
-128 + 8z + z2 = 128 + -128

Combine like terms: 128 + -128 = 0
-128 + 8z + z2 = 0

Factor a trinomial.
(-16 + -1z)(8 + -1z) = 0

Subproblem 1
Set the factor '(-16 + -1z)' equal to zero and attempt to solve:

Simplifying
-16 + -1z = 0

Solving
-16 + -1z = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1z = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1z = 0 + 16
-1z = 0 + 16

Combine like terms: 0 + 16 = 16
-1z = 16

Divide each side by '-1'.
z = -16

Simplifying
z = -16
Subproblem 2
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
Solution
z = {-16, 8}