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Simplifying (5x + -6)(6x + 9) = 0 Reorder the terms: (-6 + 5x)(6x + 9) = 0 Reorder the terms: (-6 + 5x)(9 + 6x) = 0 Multiply (-6 + 5x) * (9 + 6x) (-6(9 + 6x) + 5x * (9 + 6x)) = 0 ((9 * -6 + 6x * -6) + 5x * (9 + 6x)) = 0 ((-54 + -36x) + 5x * (9 + 6x)) = 0 (-54 + -36x + (9 * 5x + 6x * 5x)) = 0 (-54 + -36x + (45x + 30x2)) = 0 Combine like terms: -36x + 45x = 9x (-54 + 9x + 30x2) = 0 Solving -54 + 9x + 30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-18 + 3x + 10x2) = 0 Factor a trinomial. 3((-3 + -2x)(6 + -5x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve: Simplifying -3 + -2x = 0 Solving -3 + -2x = 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 + -2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2x = 0 + 3 -2x = 0 + 3 Combine like terms: 0 + 3 = 3 -2x = 3 Divide each side by '-2'. x = -1.5 Simplifying x = -1.5Subproblem 2
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 = 1.2Solution
x = {-1.5, 1.2}
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