3[(x-2)(x-2)]=12

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Solution for 3[(x-2)(x-2)]=12 equation: 


Simplifying
3[(x + -2)(x + -2)] = 12

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

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

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

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

Add '-12' to each side of the equation.
12 + -12x + -12 + 3x2 = 12 + -12

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

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

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

Solving
-12x + 3x2 = 0

Solving for variable 'x'.

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

Ignore the factor 3.

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 '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

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

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

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

Simplifying
x = 4
Solution
x = {0, 4}

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