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Simplifying (9x + -3)(5x + 6) = 0 Reorder the terms: (-3 + 9x)(5x + 6) = 0 Reorder the terms: (-3 + 9x)(6 + 5x) = 0 Multiply (-3 + 9x) * (6 + 5x) (-3(6 + 5x) + 9x * (6 + 5x)) = 0 ((6 * -3 + 5x * -3) + 9x * (6 + 5x)) = 0 ((-18 + -15x) + 9x * (6 + 5x)) = 0 (-18 + -15x + (6 * 9x + 5x * 9x)) = 0 (-18 + -15x + (54x + 45x2)) = 0 Combine like terms: -15x + 54x = 39x (-18 + 39x + 45x2) = 0 Solving -18 + 39x + 45x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + 13x + 15x2) = 0 Factor a trinomial. 3((-6 + -5x)(1 + -3x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + -5x)' equal to zero and attempt to solve: Simplifying -6 + -5x = 0 Solving -6 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -5x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5x = 0 + 6 -5x = 0 + 6 Combine like terms: 0 + 6 = 6 -5x = 6 Divide each side by '-5'. x = -1.2 Simplifying x = -1.2Subproblem 2
Set the factor '(1 + -3x)' equal to zero and attempt to solve: Simplifying 1 + -3x = 0 Solving 1 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3x = 0 + -1 -3x = 0 + -1 Combine like terms: 0 + -1 = -1 -3x = -1 Divide each side by '-3'. x = 0.3333333333 Simplifying x = 0.3333333333Solution
x = {-1.2, 0.3333333333}
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