0=12x-36-x^2

Solution for 0=12x-36-x^2 equation:

Simplifying
0 = 12x + -36 + -1x2

Reorder the terms:
0 = -36 + 12x + -1x2

Solving
0 = -36 + 12x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 36 = 36
36 + -12x + x2 = -36 + 12x + -1x2 + 36 + -12x + x2

Reorder the terms:
36 + -12x + x2 = -36 + 36 + 12x + -12x + -1x2 + x2

Combine like terms: -36 + 36 = 0
36 + -12x + x2 = 0 + 12x + -12x + -1x2 + x2
36 + -12x + x2 = 12x + -12x + -1x2 + x2

Combine like terms: 12x + -12x = 0
36 + -12x + x2 = 0 + -1x2 + x2
36 + -12x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
36 + -12x + x2 = 0

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

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

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

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

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

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

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

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

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

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

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

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

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

Simplifying
x = 6
Solution
x = {6, 6}