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

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


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

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

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

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

Combine like terms: 2x + -6x = -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.
(-3 + -1x)(7 + -1x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-3, 7}

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