z^2+35=12z-1

Solution for z^2+35=12z-1 equation:

Simplifying
z2 + 35 = 12z + -1

Reorder the terms:
35 + z2 = 12z + -1

Reorder the terms:
35 + z2 = -1 + 12z

Solving
35 + z2 = -1 + 12z

Solving for variable 'z'.

Reorder the terms:
35 + 1 + -12z + z2 = -1 + 12z + 1 + -12z

Combine like terms: 35 + 1 = 36
36 + -12z + z2 = -1 + 12z + 1 + -12z

Reorder the terms:
36 + -12z + z2 = -1 + 1 + 12z + -12z

Combine like terms: -1 + 1 = 0
36 + -12z + z2 = 0 + 12z + -12z
36 + -12z + z2 = 12z + -12z

Combine like terms: 12z + -12z = 0
36 + -12z + z2 = 0

Factor a trinomial.
(6 + -1z)(6 + -1z) = 0

Subproblem 1
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {6, 6}