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Simplifying (2x + 6)(3x + -15) = 0 Reorder the terms: (6 + 2x)(3x + -15) = 0 Reorder the terms: (6 + 2x)(-15 + 3x) = 0 Multiply (6 + 2x) * (-15 + 3x) (6(-15 + 3x) + 2x * (-15 + 3x)) = 0 ((-15 * 6 + 3x * 6) + 2x * (-15 + 3x)) = 0 ((-90 + 18x) + 2x * (-15 + 3x)) = 0 (-90 + 18x + (-15 * 2x + 3x * 2x)) = 0 (-90 + 18x + (-30x + 6x2)) = 0 Combine like terms: 18x + -30x = -12x (-90 + -12x + 6x2) = 0 Solving -90 + -12x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-15 + -2x + x2) = 0 Factor a trinomial. 6((-3 + -1x)(5 + -1x)) = 0 Ignore the factor 6.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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-3, 5}
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