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Simplifying (15x + -24)(45x + 54) = 0 Reorder the terms: (-24 + 15x)(45x + 54) = 0 Reorder the terms: (-24 + 15x)(54 + 45x) = 0 Multiply (-24 + 15x) * (54 + 45x) (-24(54 + 45x) + 15x * (54 + 45x)) = 0 ((54 * -24 + 45x * -24) + 15x * (54 + 45x)) = 0 ((-1296 + -1080x) + 15x * (54 + 45x)) = 0 (-1296 + -1080x + (54 * 15x + 45x * 15x)) = 0 (-1296 + -1080x + (810x + 675x2)) = 0 Combine like terms: -1080x + 810x = -270x (-1296 + -270x + 675x2) = 0 Solving -1296 + -270x + 675x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '27'. 27(-48 + -10x + 25x2) = 0 Factor a trinomial. 27((-6 + -5x)(8 + -5x)) = 0 Ignore the factor 27.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 '(8 + -5x)' equal to zero and attempt to solve: Simplifying 8 + -5x = 0 Solving 8 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5x = 0 + -8 -5x = 0 + -8 Combine like terms: 0 + -8 = -8 -5x = -8 Divide each side by '-5'. x = 1.6 Simplifying x = 1.6Solution
x = {-1.2, 1.6}
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