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Simplifying (3x + -4)(2x + 6)(-5x) = 0 Reorder the terms: (-4 + 3x)(2x + 6)(-5x) = 0 Reorder the terms: (-4 + 3x)(6 + 2x)(-5x) = 0 Remove parenthesis around (-5x) (-4 + 3x)(6 + 2x) * -5x = 0 Reorder the terms for easier multiplication: -5x(-4 + 3x)(6 + 2x) = 0 Multiply (-4 + 3x) * (6 + 2x) -5x(-4(6 + 2x) + 3x * (6 + 2x)) = 0 -5x((6 * -4 + 2x * -4) + 3x * (6 + 2x)) = 0 -5x((-24 + -8x) + 3x * (6 + 2x)) = 0 -5x(-24 + -8x + (6 * 3x + 2x * 3x)) = 0 -5x(-24 + -8x + (18x + 6x2)) = 0 Combine like terms: -8x + 18x = 10x -5x(-24 + 10x + 6x2) = 0 (-24 * -5x + 10x * -5x + 6x2 * -5x) = 0 (120x + -50x2 + -30x3) = 0 Solving 120x + -50x2 + -30x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10x'. 10x(12 + -5x + -3x2) = 0 Factor a trinomial. 10x((4 + -3x)(3 + x)) = 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 '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333Subproblem 3
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {0, 1.333333333, -3}
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