9(x-6)(x-6)=36

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Solution for 9(x-6)(x-6)=36 equation: 


Simplifying
9(x + -6)(x + -6) = 36

Reorder the terms:
9(-6 + x)(x + -6) = 36

Reorder the terms:
9(-6 + x)(-6 + x) = 36

Multiply (-6 + x) * (-6 + x)
9(-6(-6 + x) + x(-6 + x)) = 36
9((-6 * -6 + x * -6) + x(-6 + x)) = 36
9((36 + -6x) + x(-6 + x)) = 36
9(36 + -6x + (-6 * x + x * x)) = 36
9(36 + -6x + (-6x + x2)) = 36

Combine like terms: -6x + -6x = -12x
9(36 + -12x + x2) = 36
(36 * 9 + -12x * 9 + x2 * 9) = 36
(324 + -108x + 9x2) = 36

Solving
324 + -108x + 9x2 = 36

Solving for variable 'x'.

Reorder the terms:
324 + -36 + -108x + 9x2 = 36 + -36

Combine like terms: 324 + -36 = 288
288 + -108x + 9x2 = 36 + -36

Combine like terms: 36 + -36 = 0
288 + -108x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(32 + -12x + x2) = 0

Factor a trinomial.
9((4 + -1x)(8 + -1x)) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {4, 8}

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