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Simplifying 3(x2 + -4x + 4) + 6(x2 + -4x + 4) = 0 Reorder the terms: 3(4 + -4x + x2) + 6(x2 + -4x + 4) = 0 (4 * 3 + -4x * 3 + x2 * 3) + 6(x2 + -4x + 4) = 0 (12 + -12x + 3x2) + 6(x2 + -4x + 4) = 0 Reorder the terms: 12 + -12x + 3x2 + 6(4 + -4x + x2) = 0 12 + -12x + 3x2 + (4 * 6 + -4x * 6 + x2 * 6) = 0 12 + -12x + 3x2 + (24 + -24x + 6x2) = 0 Reorder the terms: 12 + 24 + -12x + -24x + 3x2 + 6x2 = 0 Combine like terms: 12 + 24 = 36 36 + -12x + -24x + 3x2 + 6x2 = 0 Combine like terms: -12x + -24x = -36x 36 + -36x + 3x2 + 6x2 = 0 Combine like terms: 3x2 + 6x2 = 9x2 36 + -36x + 9x2 = 0 Solving 36 + -36x + 9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '9'. 9(4 + -4x + x2) = 0 Factor a trinomial. 9((2 + -1x)(2 + -1x)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {2, 2}
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