(x+6)(x-3)=22

Solution for (x+6)(x-3)=22 equation:

Simplifying
(x + 6)(x + -3) = 22

Reorder the terms:
(6 + x)(x + -3) = 22

Reorder the terms:
(6 + x)(-3 + x) = 22

Multiply (6 + x) * (-3 + x)
(6(-3 + x) + x(-3 + x)) = 22
((-3 * 6 + x * 6) + x(-3 + x)) = 22
((-18 + 6x) + x(-3 + x)) = 22
(-18 + 6x + (-3 * x + x * x)) = 22
(-18 + 6x + (-3x + x2)) = 22

Combine like terms: 6x + -3x = 3x
(-18 + 3x + x2) = 22

Solving
-18 + 3x + x2 = 22

Solving for variable 'x'.

Reorder the terms:
-18 + -22 + 3x + x2 = 22 + -22

Combine like terms: -18 + -22 = -40
-40 + 3x + x2 = 22 + -22

Combine like terms: 22 + -22 = 0
-40 + 3x + x2 = 0

Factor a trinomial.
(-8 + -1x)(5 + -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 '(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 = {-8, 5}