(x+6)(x-2)=9

Solution for (x+6)(x-2)=9 equation:

Simplifying
(x + 6)(x + -2) = 9

Reorder the terms:
(6 + x)(x + -2) = 9

Reorder the terms:
(6 + x)(-2 + x) = 9

Multiply (6 + x) * (-2 + x)
(6(-2 + x) + x(-2 + x)) = 9
((-2 * 6 + x * 6) + x(-2 + x)) = 9
((-12 + 6x) + x(-2 + x)) = 9
(-12 + 6x + (-2 * x + x * x)) = 9
(-12 + 6x + (-2x + x2)) = 9

Combine like terms: 6x + -2x = 4x
(-12 + 4x + x2) = 9

Solving
-12 + 4x + x2 = 9

Solving for variable 'x'.

Reorder the terms:
-12 + -9 + 4x + x2 = 9 + -9

Combine like terms: -12 + -9 = -21
-21 + 4x + x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-21 + 4x + x2 = 0

Factor a trinomial.
(-7 + -1x)(3 + -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 '(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 = {-7, 3}