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Simplifying 9(9 + -4x2)(64x3 + -144x) = 0 Reorder the terms: 9(9 + -4x2)(-144x + 64x3) = 0 Multiply (9 + -4x2) * (-144x + 64x3) 9(9(-144x + 64x3) + -4x2 * (-144x + 64x3)) = 0 9((-144x * 9 + 64x3 * 9) + -4x2 * (-144x + 64x3)) = 0 9((-1296x + 576x3) + -4x2 * (-144x + 64x3)) = 0 9(-1296x + 576x3 + (-144x * -4x2 + 64x3 * -4x2)) = 0 9(-1296x + 576x3 + (576x3 + -256x5)) = 0 Combine like terms: 576x3 + 576x3 = 1152x3 9(-1296x + 1152x3 + -256x5) = 0 (-1296x * 9 + 1152x3 * 9 + -256x5 * 9) = 0 (-11664x + 10368x3 + -2304x5) = 0 Solving -11664x + 10368x3 + -2304x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '144x'. 144x(-81 + 72x2 + -16x4) = 0 Factor a trinomial. 144x((-9 + 4x2)(9 + -4x2)) = 0 Factor a difference between two squares. 144x(((3 + 2x)(-3 + 2x))(9 + -4x2)) = 0 Factor a difference between two squares. 144x(((3 + 2x)(3 + -2x))(3 + 2x)(-3 + 2x)) = 0 Ignore the factor 144.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 '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 3
Set the factor '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 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 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Divide each side by '2'. x = 1.5 Simplifying x = 1.5Subproblem 4
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 5
Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5Solution
x = {0, -1.5, 1.5, -1.5, 1.5}
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