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

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

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

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

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

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

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

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

Solving for variable 'x'.

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

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

Combine like terms: -2x + 2x = 0
-42 + 1x + x2 = 0

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}