x^2-12x^2+36=(x-6)(x-6)

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Solution for x^2-12x^2+36=(x-6)(x-6) equation: 


Simplifying
x2 + -12x2 + 36 = (x + -6)(x + -6)

Reorder the terms:
36 + x2 + -12x2 = (x + -6)(x + -6)

Combine like terms: x2 + -12x2 = -11x2
36 + -11x2 = (x + -6)(x + -6)

Reorder the terms:
36 + -11x2 = (-6 + x)(x + -6)

Reorder the terms:
36 + -11x2 = (-6 + x)(-6 + x)

Multiply (-6 + x) * (-6 + x)
36 + -11x2 = (-6(-6 + x) + x(-6 + x))
36 + -11x2 = ((-6 * -6 + x * -6) + x(-6 + x))
36 + -11x2 = ((36 + -6x) + x(-6 + x))
36 + -11x2 = (36 + -6x + (-6 * x + x * x))
36 + -11x2 = (36 + -6x + (-6x + x2))

Combine like terms: -6x + -6x = -12x
36 + -11x2 = (36 + -12x + x2)

Add '-36' to each side of the equation.
36 + -36 + -11x2 = 36 + -12x + -36 + x2

Combine like terms: 36 + -36 = 0
0 + -11x2 = 36 + -12x + -36 + x2
-11x2 = 36 + -12x + -36 + x2

Reorder the terms:
-11x2 = 36 + -36 + -12x + x2

Combine like terms: 36 + -36 = 0
-11x2 = 0 + -12x + x2
-11x2 = -12x + x2

Solving
-11x2 = -12x + x2

Solving for variable 'x'.

Reorder the terms:
12x + -11x2 + -1x2 = -12x + x2 + 12x + -1x2

Combine like terms: -11x2 + -1x2 = -12x2
12x + -12x2 = -12x + x2 + 12x + -1x2

Reorder the terms:
12x + -12x2 = -12x + 12x + x2 + -1x2

Combine like terms: -12x + 12x = 0
12x + -12x2 = 0 + x2 + -1x2
12x + -12x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '12x'.
12x(1 + -1x) = 0

Ignore the factor 12.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {0, 1}

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