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Simplifying (3x + 9)(4x + -20) = 0 Reorder the terms: (9 + 3x)(4x + -20) = 0 Reorder the terms: (9 + 3x)(-20 + 4x) = 0 Multiply (9 + 3x) * (-20 + 4x) (9(-20 + 4x) + 3x * (-20 + 4x)) = 0 ((-20 * 9 + 4x * 9) + 3x * (-20 + 4x)) = 0 ((-180 + 36x) + 3x * (-20 + 4x)) = 0 (-180 + 36x + (-20 * 3x + 4x * 3x)) = 0 (-180 + 36x + (-60x + 12x2)) = 0 Combine like terms: 36x + -60x = -24x (-180 + -24x + 12x2) = 0 Solving -180 + -24x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(-15 + -2x + x2) = 0 Factor a trinomial. 12((-3 + -1x)(5 + -1x)) = 0 Ignore the factor 12.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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