3(x-2)(x-2)+12=0

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Solution for 3(x-2)(x-2)+12=0 equation: 


Simplifying
3(x + -2)(x + -2) + 12 = 0

Reorder the terms:
3(-2 + x)(x + -2) + 12 = 0

Reorder the terms:
3(-2 + x)(-2 + x) + 12 = 0

Multiply (-2 + x) * (-2 + x)
3(-2(-2 + x) + x(-2 + x)) + 12 = 0
3((-2 * -2 + x * -2) + x(-2 + x)) + 12 = 0
3((4 + -2x) + x(-2 + x)) + 12 = 0
3(4 + -2x + (-2 * x + x * x)) + 12 = 0
3(4 + -2x + (-2x + x2)) + 12 = 0

Combine like terms: -2x + -2x = -4x
3(4 + -4x + x2) + 12 = 0
(4 * 3 + -4x * 3 + x2 * 3) + 12 = 0
(12 + -12x + 3x2) + 12 = 0

Reorder the terms:
12 + 12 + -12x + 3x2 = 0

Combine like terms: 12 + 12 = 24
24 + -12x + 3x2 = 0

Solving
24 + -12x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + -4x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(8 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
8 + -4x + x2 = 0

Solving
8 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -4x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -4x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -4x + x2 = 0 + -8
-4x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-4x + x2 = -8

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -8 + 4

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

Combine like terms: -8 + 4 = -4
4 + -4x + x2 = -4

Factor a perfect square on the left side:
(x + -2)(x + -2) = -4

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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