(x-6)=(x-6)*(x+6)

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Solution for (x-6)=(x-6)*(x+6) equation: 


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

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

Remove parenthesis around (-6 + x)
-6 + x = (x + -6)(x + 6)

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

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

Multiply (-6 + x) * (6 + x)
-6 + x = (-6(6 + x) + x(6 + x))
-6 + x = ((6 * -6 + x * -6) + x(6 + x))
-6 + x = ((-36 + -6x) + x(6 + x))
-6 + x = (-36 + -6x + (6 * x + x * x))
-6 + x = (-36 + -6x + (6x + x2))

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

Solving
-6 + x = -36 + x2

Solving for variable 'x'.

Reorder the terms:
-6 + 36 + x + -1x2 = -36 + x2 + 36 + -1x2

Combine like terms: -6 + 36 = 30
30 + x + -1x2 = -36 + x2 + 36 + -1x2

Reorder the terms:
30 + x + -1x2 = -36 + 36 + x2 + -1x2

Combine like terms: -36 + 36 = 0
30 + x + -1x2 = 0 + x2 + -1x2
30 + x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
30 + x + -1x2 = 0

Factor a trinomial.
(6 + -1x)(5 + x) = 0


Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {6, -5}

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