z^2=12z-35

Solution for z^2=12z-35 equation:

Simplifying
z2 = 12z + -35

Reorder the terms:
z2 = -35 + 12z

Solving
z2 = -35 + 12z

Solving for variable 'z'.

Reorder the terms:
35 + -12z + z2 = -35 + 12z + 35 + -12z

Reorder the terms:
35 + -12z + z2 = -35 + 35 + 12z + -12z

Combine like terms: -35 + 35 = 0
35 + -12z + z2 = 0 + 12z + -12z
35 + -12z + z2 = 12z + -12z

Combine like terms: 12z + -12z = 0
35 + -12z + z2 = 0

Factor a trinomial.
(5 + -1z)(7 + -1z) = 0

Subproblem 1
Set the factor '(5 + -1z)' equal to zero and attempt to solve:

Simplifying
5 + -1z = 0

Solving
5 + -1z = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5
Subproblem 2
Set the factor '(7 + -1z)' equal to zero and attempt to solve:

Simplifying
7 + -1z = 0

Solving
7 + -1z = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1z = 0 + -7
-1z = 0 + -7

Combine like terms: 0 + -7 = -7
-1z = -7

Divide each side by '-1'.
z = 7

Simplifying
z = 7
Solution
z = {5, 7}