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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 + -1x2) = 0 Factor a trinomial. 6((3 + -1x)(5 + x)) = 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 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {3, -5}
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