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Simplifying (x3 + -9x)(x2 + -3) + 9x = x3 Reorder the terms: (-9x + x3)(x2 + -3) + 9x = x3 Reorder the terms: (-9x + x3)(-3 + x2) + 9x = x3 Multiply (-9x + x3) * (-3 + x2) (-9x * (-3 + x2) + x3(-3 + x2)) + 9x = x3 ((-3 * -9x + x2 * -9x) + x3(-3 + x2)) + 9x = x3 ((27x + -9x3) + x3(-3 + x2)) + 9x = x3 (27x + -9x3 + (-3 * x3 + x2 * x3)) + 9x = x3 (27x + -9x3 + (-3x3 + x5)) + 9x = x3 Combine like terms: -9x3 + -3x3 = -12x3 (27x + -12x3 + x5) + 9x = x3 Reorder the terms: 27x + 9x + -12x3 + x5 = x3 Combine like terms: 27x + 9x = 36x 36x + -12x3 + x5 = x3 Solving 36x + -12x3 + x5 = x3 Solving for variable 'x'. Reorder the terms: 36x + -12x3 + -1x3 + x5 = x3 + -1x3 Combine like terms: -12x3 + -1x3 = -13x3 36x + -13x3 + x5 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 36x + -13x3 + x5 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(36 + -13x2 + x4) = 0 Factor a trinomial. x((4 + -1x2)(9 + -1x2)) = 0 Factor a difference between two squares. x(((2 + x)(2 + -1x))(9 + -1x2)) = 0 Factor a difference between two squares. x(((3 + x)(3 + -1x))(2 + x)(2 + -1x)) = 0Subproblem 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 4
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 = -3Subproblem 5
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {0, -2, 2, -3, 3}
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