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Simplifying 4x(x + -5)(x + 6) = 0 Reorder the terms: 4x(-5 + x)(x + 6) = 0 Reorder the terms: 4x(-5 + x)(6 + x) = 0 Multiply (-5 + x) * (6 + x) 4x(-5(6 + x) + x(6 + x)) = 0 4x((6 * -5 + x * -5) + x(6 + x)) = 0 4x((-30 + -5x) + x(6 + x)) = 0 4x(-30 + -5x + (6 * x + x * x)) = 0 4x(-30 + -5x + (6x + x2)) = 0 Combine like terms: -5x + 6x = 1x 4x(-30 + 1x + x2) = 0 (-30 * 4x + 1x * 4x + x2 * 4x) = 0 (-120x + 4x2 + 4x3) = 0 Solving -120x + 4x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-30 + x + x2) = 0 Factor a trinomial. 4x((-6 + -1x)(5 + -1x)) = 0 Ignore the factor 4.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 '(-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 = -6Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {0, -6, 5}
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