z*z+32=12z

Solution for z*z+32=12z equation:

Simplifying
z * z + 32 = 12z

Multiply z * z
z2 + 32 = 12z

Reorder the terms:
32 + z2 = 12z

Solving
32 + z2 = 12z

Solving for variable 'z'.

Reorder the terms:
32 + -12z + z2 = 12z + -12z

Combine like terms: 12z + -12z = 0
32 + -12z + z2 = 0

Factor a trinomial.
(4 + -1z)(8 + -1z) = 0

Subproblem 1
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4
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 = {4, 8}