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Simplifying 4(x + 2)(x + 3) + -6x = 12 Reorder the terms: 4(2 + x)(x + 3) + -6x = 12 Reorder the terms: 4(2 + x)(3 + x) + -6x = 12 Multiply (2 + x) * (3 + x) 4(2(3 + x) + x(3 + x)) + -6x = 12 4((3 * 2 + x * 2) + x(3 + x)) + -6x = 12 4((6 + 2x) + x(3 + x)) + -6x = 12 4(6 + 2x + (3 * x + x * x)) + -6x = 12 4(6 + 2x + (3x + x2)) + -6x = 12 Combine like terms: 2x + 3x = 5x 4(6 + 5x + x2) + -6x = 12 (6 * 4 + 5x * 4 + x2 * 4) + -6x = 12 (24 + 20x + 4x2) + -6x = 12 Reorder the terms: 24 + 20x + -6x + 4x2 = 12 Combine like terms: 20x + -6x = 14x 24 + 14x + 4x2 = 12 Solving 24 + 14x + 4x2 = 12 Solving for variable 'x'. Reorder the terms: 24 + -12 + 14x + 4x2 = 12 + -12 Combine like terms: 24 + -12 = 12 12 + 14x + 4x2 = 12 + -12 Combine like terms: 12 + -12 = 0 12 + 14x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + 7x + 2x2) = 0 Factor a trinomial. 2((2 + x)(3 + 2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {-2, -1.5}
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