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Simplifying (3x + 3)(4x + -6) = 0 Reorder the terms: (3 + 3x)(4x + -6) = 0 Reorder the terms: (3 + 3x)(-6 + 4x) = 0 Multiply (3 + 3x) * (-6 + 4x) (3(-6 + 4x) + 3x * (-6 + 4x)) = 0 ((-6 * 3 + 4x * 3) + 3x * (-6 + 4x)) = 0 ((-18 + 12x) + 3x * (-6 + 4x)) = 0 (-18 + 12x + (-6 * 3x + 4x * 3x)) = 0 (-18 + 12x + (-18x + 12x2)) = 0 Combine like terms: 12x + -18x = -6x (-18 + -6x + 12x2) = 0 Solving -18 + -6x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-3 + -1x + 2x2) = 0 Factor a trinomial. 6((-1 + -1x)(3 + -2x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 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 = {-1, 1.5}
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