x^2+12x+36-(2x-7)(x+6)=0

Solution for x^2+12x+36-(2x-7)(x+6)=0 equation:

Simplifying
x2 + 12x + 36 + -1(2x + -7)(x + 6) = 0

Reorder the terms:
x2 + 12x + 36 + -1(-7 + 2x)(x + 6) = 0

Reorder the terms:
x2 + 12x + 36 + -1(-7 + 2x)(6 + x) = 0

Multiply (-7 + 2x) * (6 + x)
x2 + 12x + 36 + -1(-7(6 + x) + 2x * (6 + x)) = 0
x2 + 12x + 36 + -1((6 * -7 + x * -7) + 2x * (6 + x)) = 0
x2 + 12x + 36 + -1((-42 + -7x) + 2x * (6 + x)) = 0
x2 + 12x + 36 + -1(-42 + -7x + (6 * 2x + x * 2x)) = 0
x2 + 12x + 36 + -1(-42 + -7x + (12x + 2x2)) = 0

Combine like terms: -7x + 12x = 5x
x2 + 12x + 36 + -1(-42 + 5x + 2x2) = 0
x2 + 12x + 36 + (-42 * -1 + 5x * -1 + 2x2 * -1) = 0
x2 + 12x + 36 + (42 + -5x + -2x2) = 0

Reorder the terms:
36 + 42 + 12x + -5x + x2 + -2x2 = 0

Combine like terms: 36 + 42 = 78
78 + 12x + -5x + x2 + -2x2 = 0

Combine like terms: 12x + -5x = 7x
78 + 7x + x2 + -2x2 = 0

Combine like terms: x2 + -2x2 = -1x2
78 + 7x + -1x2 = 0

Solving
78 + 7x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(13 + -1x)(6 + x) = 0

Subproblem 1
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
Solution
x = {13, -6}