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Simplifying (6 + 3x)(4x + -12) = 0 Reorder the terms: (6 + 3x)(-12 + 4x) = 0 Multiply (6 + 3x) * (-12 + 4x) (6(-12 + 4x) + 3x * (-12 + 4x)) = 0 ((-12 * 6 + 4x * 6) + 3x * (-12 + 4x)) = 0 ((-72 + 24x) + 3x * (-12 + 4x)) = 0 (-72 + 24x + (-12 * 3x + 4x * 3x)) = 0 (-72 + 24x + (-36x + 12x2)) = 0 Combine like terms: 24x + -36x = -12x (-72 + -12x + 12x2) = 0 Solving -72 + -12x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(-6 + -1x + x2) = 0 Factor a trinomial. 12((-2 + -1x)(3 + -1x)) = 0 Ignore the factor 12.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 '(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 = {-2, 3}
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