(x-7)(x+6)=-22

Solution for (x-7)(x+6)=-22 equation:

Simplifying
(x + -7)(x + 6) = -22

Reorder the terms:
(-7 + x)(x + 6) = -22

Reorder the terms:
(-7 + x)(6 + x) = -22

Multiply (-7 + x) * (6 + x)
(-7(6 + x) + x(6 + x)) = -22
((6 * -7 + x * -7) + x(6 + x)) = -22
((-42 + -7x) + x(6 + x)) = -22
(-42 + -7x + (6 * x + x * x)) = -22
(-42 + -7x + (6x + x2)) = -22

Combine like terms: -7x + 6x = -1x
(-42 + -1x + x2) = -22

Solving
-42 + -1x + x2 = -22

Solving for variable 'x'.

Reorder the terms:
-42 + 22 + -1x + x2 = -22 + 22

Combine like terms: -42 + 22 = -20
-20 + -1x + x2 = -22 + 22

Combine like terms: -22 + 22 = 0
-20 + -1x + x2 = 0

Factor a trinomial.
(-4 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
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 = {-4, 5}