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Simplifying 10x(2x + -9)(x + -6) = 0 Reorder the terms: 10x(-9 + 2x)(x + -6) = 0 Reorder the terms: 10x(-9 + 2x)(-6 + x) = 0 Multiply (-9 + 2x) * (-6 + x) 10x(-9(-6 + x) + 2x * (-6 + x)) = 0 10x((-6 * -9 + x * -9) + 2x * (-6 + x)) = 0 10x((54 + -9x) + 2x * (-6 + x)) = 0 10x(54 + -9x + (-6 * 2x + x * 2x)) = 0 10x(54 + -9x + (-12x + 2x2)) = 0 Combine like terms: -9x + -12x = -21x 10x(54 + -21x + 2x2) = 0 (54 * 10x + -21x * 10x + 2x2 * 10x) = 0 (540x + -210x2 + 20x3) = 0 Solving 540x + -210x2 + 20x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10x'. 10x(54 + -21x + 2x2) = 0 Factor a trinomial. 10x((9 + -2x)(6 + -1x)) = 0 Ignore the factor 10.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(9 + -2x)' equal to zero and attempt to solve: Simplifying 9 + -2x = 0 Solving 9 + -2x = 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 + -2x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2x = 0 + -9 -2x = 0 + -9 Combine like terms: 0 + -9 = -9 -2x = -9 Divide each side by '-2'. x = 4.5 Simplifying x = 4.5Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {0, 4.5, 6}
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