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Simplifying 4x(4x + -9)(9x + 5) = 0 Reorder the terms: 4x(-9 + 4x)(9x + 5) = 0 Reorder the terms: 4x(-9 + 4x)(5 + 9x) = 0 Multiply (-9 + 4x) * (5 + 9x) 4x(-9(5 + 9x) + 4x * (5 + 9x)) = 0 4x((5 * -9 + 9x * -9) + 4x * (5 + 9x)) = 0 4x((-45 + -81x) + 4x * (5 + 9x)) = 0 4x(-45 + -81x + (5 * 4x + 9x * 4x)) = 0 4x(-45 + -81x + (20x + 36x2)) = 0 Combine like terms: -81x + 20x = -61x 4x(-45 + -61x + 36x2) = 0 (-45 * 4x + -61x * 4x + 36x2 * 4x) = 0 (-180x + -244x2 + 144x3) = 0 Solving -180x + -244x2 + 144x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-45 + -61x + 36x2) = 0 Factor a trinomial. 4x((-5 + -9x)(9 + -4x)) = 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 '(-5 + -9x)' equal to zero and attempt to solve: Simplifying -5 + -9x = 0 Solving -5 + -9x = 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 + -9x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -9x = 0 + 5 -9x = 0 + 5 Combine like terms: 0 + 5 = 5 -9x = 5 Divide each side by '-9'. x = -0.5555555556 Simplifying x = -0.5555555556Subproblem 3
Set the factor '(9 + -4x)' equal to zero and attempt to solve: Simplifying 9 + -4x = 0 Solving 9 + -4x = 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 + -4x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4x = 0 + -9 -4x = 0 + -9 Combine like terms: 0 + -9 = -9 -4x = -9 Divide each side by '-4'. x = 2.25 Simplifying x = 2.25Solution
x = {0, -0.5555555556, 2.25}
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