(x-7)(x+6)=-6(x+3)

Solution for (x-7)(x+6)=-6(x+3) equation:

Simplifying
(x + -7)(x + 6) = -6(x + 3)

Reorder the terms:
(-7 + x)(x + 6) = -6(x + 3)

Reorder the terms:
(-7 + x)(6 + x) = -6(x + 3)

Multiply (-7 + x) * (6 + x)
(-7(6 + x) + x(6 + x)) = -6(x + 3)
((6 * -7 + x * -7) + x(6 + x)) = -6(x + 3)
((-42 + -7x) + x(6 + x)) = -6(x + 3)
(-42 + -7x + (6 * x + x * x)) = -6(x + 3)
(-42 + -7x + (6x + x2)) = -6(x + 3)

Combine like terms: -7x + 6x = -1x
(-42 + -1x + x2) = -6(x + 3)

Reorder the terms:
-42 + -1x + x2 = -6(3 + x)
-42 + -1x + x2 = (3 * -6 + x * -6)
-42 + -1x + x2 = (-18 + -6x)

Solving
-42 + -1x + x2 = -18 + -6x

Solving for variable 'x'.

Reorder the terms:
-42 + 18 + -1x + 6x + x2 = -18 + -6x + 18 + 6x

Combine like terms: -42 + 18 = -24
-24 + -1x + 6x + x2 = -18 + -6x + 18 + 6x

Combine like terms: -1x + 6x = 5x
-24 + 5x + x2 = -18 + -6x + 18 + 6x

Reorder the terms:
-24 + 5x + x2 = -18 + 18 + -6x + 6x

Combine like terms: -18 + 18 = 0
-24 + 5x + x2 = 0 + -6x + 6x
-24 + 5x + x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-24 + 5x + x2 = 0

Factor a trinomial.
(-8 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
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 = {-8, 3}