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Simplifying (3x + 9)(-2x + 10) = 0 Reorder the terms: (9 + 3x)(-2x + 10) = 0 Reorder the terms: (9 + 3x)(10 + -2x) = 0 Multiply (9 + 3x) * (10 + -2x) (9(10 + -2x) + 3x * (10 + -2x)) = 0 ((10 * 9 + -2x * 9) + 3x * (10 + -2x)) = 0 ((90 + -18x) + 3x * (10 + -2x)) = 0 (90 + -18x + (10 * 3x + -2x * 3x)) = 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((5 + -1x)(3 + x)) = 0 Ignore the factor 6.Subproblem 1
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 = 5Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {5, -3}
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