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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 = 48x (-90 + 48x + -6x2) = 0 Solving -90 + 48x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(-15 + 8x + -1x2) = 0 Factor a trinomial. 6((-5 + x)(3 + -1x)) = 0 Ignore the factor 6.Subproblem 1
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 = 5Subproblem 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 = {5, 3}
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