(x+6)(x-6)-8=1-4x

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Solution for (x+6)(x-6)-8=1-4x equation: 


Simplifying
(x + 6)(x + -6) + -8 = 1 + -4x

Reorder the terms:
(6 + x)(x + -6) + -8 = 1 + -4x

Reorder the terms:
(6 + x)(-6 + x) + -8 = 1 + -4x

Multiply (6 + x) * (-6 + x)
(6(-6 + x) + x(-6 + x)) + -8 = 1 + -4x
((-6 * 6 + x * 6) + x(-6 + x)) + -8 = 1 + -4x
((-36 + 6x) + x(-6 + x)) + -8 = 1 + -4x
(-36 + 6x + (-6 * x + x * x)) + -8 = 1 + -4x
(-36 + 6x + (-6x + x2)) + -8 = 1 + -4x

Combine like terms: 6x + -6x = 0
(-36 + 0 + x2) + -8 = 1 + -4x
(-36 + x2) + -8 = 1 + -4x

Reorder the terms:
-36 + -8 + x2 = 1 + -4x

Combine like terms: -36 + -8 = -44
-44 + x2 = 1 + -4x

Solving
-44 + x2 = 1 + -4x

Solving for variable 'x'.

Reorder the terms:
-44 + -1 + 4x + x2 = 1 + -4x + -1 + 4x

Combine like terms: -44 + -1 = -45
-45 + 4x + x2 = 1 + -4x + -1 + 4x

Reorder the terms:
-45 + 4x + x2 = 1 + -1 + -4x + 4x

Combine like terms: 1 + -1 = 0
-45 + 4x + x2 = 0 + -4x + 4x
-45 + 4x + x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-45 + 4x + x2 = 0

Factor a trinomial.
(-9 + -1x)(5 + -1x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

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 = {-9, 5}

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