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Simplifying (4x + 6)(5x + -9) = 0 Reorder the terms: (6 + 4x)(5x + -9) = 0 Reorder the terms: (6 + 4x)(-9 + 5x) = 0 Multiply (6 + 4x) * (-9 + 5x) (6(-9 + 5x) + 4x * (-9 + 5x)) = 0 ((-9 * 6 + 5x * 6) + 4x * (-9 + 5x)) = 0 ((-54 + 30x) + 4x * (-9 + 5x)) = 0 (-54 + 30x + (-9 * 4x + 5x * 4x)) = 0 (-54 + 30x + (-36x + 20x2)) = 0 Combine like terms: 30x + -36x = -6x (-54 + -6x + 20x2) = 0 Solving -54 + -6x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + -3x + 10x2) = 0 Factor a trinomial. 2((-3 + -2x)(9 + -5x)) = 0 Ignore the factor 2.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 '(9 + -5x)' equal to zero and attempt to solve: Simplifying 9 + -5x = 0 Solving 9 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -5x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5x = 0 + -9 -5x = 0 + -9 Combine like terms: 0 + -9 = -9 -5x = -9 Divide each side by '-5'. x = 1.8 Simplifying x = 1.8Solution
x = {-1.5, 1.8}
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