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Simplifying 3(x + -2)(x + -2) + 3 = 6x + -12 Reorder the terms: 3(-2 + x)(x + -2) + 3 = 6x + -12 Reorder the terms: 3(-2 + x)(-2 + x) + 3 = 6x + -12 Multiply (-2 + x) * (-2 + x) 3(-2(-2 + x) + x(-2 + x)) + 3 = 6x + -12 3((-2 * -2 + x * -2) + x(-2 + x)) + 3 = 6x + -12 3((4 + -2x) + x(-2 + x)) + 3 = 6x + -12 3(4 + -2x + (-2 * x + x * x)) + 3 = 6x + -12 3(4 + -2x + (-2x + x2)) + 3 = 6x + -12 Combine like terms: -2x + -2x = -4x 3(4 + -4x + x2) + 3 = 6x + -12 (4 * 3 + -4x * 3 + x2 * 3) + 3 = 6x + -12 (12 + -12x + 3x2) + 3 = 6x + -12 Reorder the terms: 12 + 3 + -12x + 3x2 = 6x + -12 Combine like terms: 12 + 3 = 15 15 + -12x + 3x2 = 6x + -12 Reorder the terms: 15 + -12x + 3x2 = -12 + 6x Solving 15 + -12x + 3x2 = -12 + 6x Solving for variable 'x'. Reorder the terms: 15 + 12 + -12x + -6x + 3x2 = -12 + 6x + 12 + -6x Combine like terms: 15 + 12 = 27 27 + -12x + -6x + 3x2 = -12 + 6x + 12 + -6x Combine like terms: -12x + -6x = -18x 27 + -18x + 3x2 = -12 + 6x + 12 + -6x Reorder the terms: 27 + -18x + 3x2 = -12 + 12 + 6x + -6x Combine like terms: -12 + 12 = 0 27 + -18x + 3x2 = 0 + 6x + -6x 27 + -18x + 3x2 = 6x + -6x Combine like terms: 6x + -6x = 0 27 + -18x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(9 + -6x + x2) = 0 Factor a trinomial. 3((3 + -1x)(3 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {3, 3}
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