(x-6)(x+7)=-2(x+12)

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

Simplifying
(x + -6)(x + 7) = -2(x + 12)

Reorder the terms:
(-6 + x)(x + 7) = -2(x + 12)

Reorder the terms:
(-6 + x)(7 + x) = -2(x + 12)

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

Combine like terms: -6x + 7x = 1x
(-42 + 1x + x2) = -2(x + 12)

Reorder the terms:
-42 + 1x + x2 = -2(12 + x)
-42 + 1x + x2 = (12 * -2 + x * -2)
-42 + 1x + x2 = (-24 + -2x)

Solving
-42 + 1x + x2 = -24 + -2x

Solving for variable 'x'.

Reorder the terms:
-42 + 24 + 1x + 2x + x2 = -24 + -2x + 24 + 2x

Combine like terms: -42 + 24 = -18
-18 + 1x + 2x + x2 = -24 + -2x + 24 + 2x

Combine like terms: 1x + 2x = 3x
-18 + 3x + x2 = -24 + -2x + 24 + 2x

Reorder the terms:
-18 + 3x + x2 = -24 + 24 + -2x + 2x

Combine like terms: -24 + 24 = 0
-18 + 3x + x2 = 0 + -2x + 2x
-18 + 3x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-18 + 3x + x2 = 0

Factor a trinomial.
(-6 + -1x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-6, 3}