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Simplifying 2(X + -2)(X + -2) + -2X + -8(X + -2) + 12 = 0 Reorder the terms: 2(-2 + X)(X + -2) + -2X + -8(X + -2) + 12 = 0 Reorder the terms: 2(-2 + X)(-2 + X) + -2X + -8(X + -2) + 12 = 0 Multiply (-2 + X) * (-2 + X) 2(-2(-2 + X) + X(-2 + X)) + -2X + -8(X + -2) + 12 = 0 2((-2 * -2 + X * -2) + X(-2 + X)) + -2X + -8(X + -2) + 12 = 0 2((4 + -2X) + X(-2 + X)) + -2X + -8(X + -2) + 12 = 0 2(4 + -2X + (-2 * X + X * X)) + -2X + -8(X + -2) + 12 = 0 2(4 + -2X + (-2X + X2)) + -2X + -8(X + -2) + 12 = 0 Combine like terms: -2X + -2X = -4X 2(4 + -4X + X2) + -2X + -8(X + -2) + 12 = 0 (4 * 2 + -4X * 2 + X2 * 2) + -2X + -8(X + -2) + 12 = 0 (8 + -8X + 2X2) + -2X + -8(X + -2) + 12 = 0 Reorder the terms: 8 + -8X + 2X2 + -2X + -8(-2 + X) + 12 = 0 8 + -8X + 2X2 + -2X + (-2 * -8 + X * -8) + 12 = 0 8 + -8X + 2X2 + -2X + (16 + -8X) + 12 = 0 Reorder the terms: 8 + 16 + 12 + -8X + -2X + -8X + 2X2 = 0 Combine like terms: 8 + 16 = 24 24 + 12 + -8X + -2X + -8X + 2X2 = 0 Combine like terms: 24 + 12 = 36 36 + -8X + -2X + -8X + 2X2 = 0 Combine like terms: -8X + -2X = -10X 36 + -10X + -8X + 2X2 = 0 Combine like terms: -10X + -8X = -18X 36 + -18X + 2X2 = 0 Solving 36 + -18X + 2X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '2'. 2(18 + -9X + X2) = 0 Factor a trinomial. 2((3 + -1X)(6 + -1X)) = 0 Ignore the factor 2.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 '(6 + -1X)' equal to zero and attempt to solve: Simplifying 6 + -1X = 0 Solving 6 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1X = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1X = 0 + -6 -1X = 0 + -6 Combine like terms: 0 + -6 = -6 -1X = -6 Divide each side by '-1'. X = 6 Simplifying X = 6Solution
X = {3, 6}
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