27(x^2-4x+4)-12=0

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Solution for 27(x^2-4x+4)-12=0 equation: 


Simplifying
27(x2 + -4x + 4) + -12 = 0

Reorder the terms:
27(4 + -4x + x2) + -12 = 0
(4 * 27 + -4x * 27 + x2 * 27) + -12 = 0
(108 + -108x + 27x2) + -12 = 0

Reorder the terms:
108 + -12 + -108x + 27x2 = 0

Combine like terms: 108 + -12 = 96
96 + -108x + 27x2 = 0

Solving
96 + -108x + 27x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(32 + -36x + 9x2) = 0

Factor a trinomial.
3((4 + -3x)(8 + -3x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 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 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 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 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {1.333333333, 2.666666667}

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