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Simplifying 5x(4x + -16)(x + 9) = 0 Reorder the terms: 5x(-16 + 4x)(x + 9) = 0 Reorder the terms: 5x(-16 + 4x)(9 + x) = 0 Multiply (-16 + 4x) * (9 + x) 5x(-16(9 + x) + 4x * (9 + x)) = 0 5x((9 * -16 + x * -16) + 4x * (9 + x)) = 0 5x((-144 + -16x) + 4x * (9 + x)) = 0 5x(-144 + -16x + (9 * 4x + x * 4x)) = 0 5x(-144 + -16x + (36x + 4x2)) = 0 Combine like terms: -16x + 36x = 20x 5x(-144 + 20x + 4x2) = 0 (-144 * 5x + 20x * 5x + 4x2 * 5x) = 0 (-720x + 100x2 + 20x3) = 0 Solving -720x + 100x2 + 20x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '20x'. 20x(-36 + 5x + x2) = 0 Factor a trinomial. 20x((-9 + -1x)(4 + -1x)) = 0 Ignore the factor 20.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 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 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 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {0, -9, 4}
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