(x+7)*(x-6)=-12

Solution for (x+7)*(x-6)=-12 equation:

Simplifying
(x + 7)(x + -6) = -12

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

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

Multiply (7 + x) * (-6 + x)
(7(-6 + x) + x(-6 + x)) = -12
((-6 * 7 + x * 7) + x(-6 + x)) = -12
((-42 + 7x) + x(-6 + x)) = -12
(-42 + 7x + (-6 * x + x * x)) = -12
(-42 + 7x + (-6x + x2)) = -12

Combine like terms: 7x + -6x = 1x
(-42 + 1x + x2) = -12

Solving
-42 + 1x + x2 = -12

Solving for variable 'x'.

Reorder the terms:
-42 + 12 + 1x + x2 = -12 + 12

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

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

Factor a trinomial.
(-6 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

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

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

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

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

Simplifying
x = 5
Solution
x = {-6, 5}