(x-5)(x+6)-12=0

Solution for (x-5)(x+6)-12=0 equation:

Simplifying
(x + -5)(x + 6) + -12 = 0

Reorder the terms:
(-5 + x)(x + 6) + -12 = 0

Reorder the terms:
(-5 + x)(6 + x) + -12 = 0

Multiply (-5 + x) * (6 + x)
(-5(6 + x) + x(6 + x)) + -12 = 0
((6 * -5 + x * -5) + x(6 + x)) + -12 = 0
((-30 + -5x) + x(6 + x)) + -12 = 0
(-30 + -5x + (6 * x + x * x)) + -12 = 0
(-30 + -5x + (6x + x2)) + -12 = 0

Combine like terms: -5x + 6x = 1x
(-30 + 1x + x2) + -12 = 0

Reorder the terms:
-30 + -12 + 1x + x2 = 0

Combine like terms: -30 + -12 = -42
-42 + 1x + x2 = 0

Solving
-42 + 1x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

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

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

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

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

Simplifying
x = -7
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 = {-7, 6}