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Simplifying (9x3 + -1x)(3x2 + 2x) = (9x3 + -4x)(3x2 + x) Reorder the terms: (-1x + 9x3)(3x2 + 2x) = (9x3 + -4x)(3x2 + x) Reorder the terms: (-1x + 9x3)(2x + 3x2) = (9x3 + -4x)(3x2 + x) Multiply (-1x + 9x3) * (2x + 3x2) (-1x * (2x + 3x2) + 9x3 * (2x + 3x2)) = (9x3 + -4x)(3x2 + x) ((2x * -1x + 3x2 * -1x) + 9x3 * (2x + 3x2)) = (9x3 + -4x)(3x2 + x) ((-2x2 + -3x3) + 9x3 * (2x + 3x2)) = (9x3 + -4x)(3x2 + x) (-2x2 + -3x3 + (2x * 9x3 + 3x2 * 9x3)) = (9x3 + -4x)(3x2 + x) (-2x2 + -3x3 + (18x4 + 27x5)) = (9x3 + -4x)(3x2 + x) (-2x2 + -3x3 + 18x4 + 27x5) = (9x3 + -4x)(3x2 + x) Reorder the terms: -2x2 + -3x3 + 18x4 + 27x5 = (-4x + 9x3)(3x2 + x) Reorder the terms: -2x2 + -3x3 + 18x4 + 27x5 = (-4x + 9x3)(x + 3x2) Multiply (-4x + 9x3) * (x + 3x2) -2x2 + -3x3 + 18x4 + 27x5 = (-4x * (x + 3x2) + 9x3 * (x + 3x2)) -2x2 + -3x3 + 18x4 + 27x5 = ((x * -4x + 3x2 * -4x) + 9x3 * (x + 3x2)) -2x2 + -3x3 + 18x4 + 27x5 = ((-4x2 + -12x3) + 9x3 * (x + 3x2)) -2x2 + -3x3 + 18x4 + 27x5 = (-4x2 + -12x3 + (x * 9x3 + 3x2 * 9x3)) -2x2 + -3x3 + 18x4 + 27x5 = (-4x2 + -12x3 + (9x4 + 27x5)) -2x2 + -3x3 + 18x4 + 27x5 = (-4x2 + -12x3 + 9x4 + 27x5) Add '-27x5' to each side of the equation. -2x2 + -3x3 + 18x4 + 27x5 + -27x5 = -4x2 + -12x3 + 9x4 + 27x5 + -27x5 Combine like terms: 27x5 + -27x5 = 0 -2x2 + -3x3 + 18x4 + 0 = -4x2 + -12x3 + 9x4 + 27x5 + -27x5 -2x2 + -3x3 + 18x4 = -4x2 + -12x3 + 9x4 + 27x5 + -27x5 Combine like terms: 27x5 + -27x5 = 0 -2x2 + -3x3 + 18x4 = -4x2 + -12x3 + 9x4 + 0 -2x2 + -3x3 + 18x4 = -4x2 + -12x3 + 9x4 Solving -2x2 + -3x3 + 18x4 = -4x2 + -12x3 + 9x4 Solving for variable 'x'. Reorder the terms: -2x2 + 4x2 + -3x3 + 12x3 + 18x4 + -9x4 = -4x2 + -12x3 + 9x4 + 4x2 + 12x3 + -9x4 Combine like terms: -2x2 + 4x2 = 2x2 2x2 + -3x3 + 12x3 + 18x4 + -9x4 = -4x2 + -12x3 + 9x4 + 4x2 + 12x3 + -9x4 Combine like terms: -3x3 + 12x3 = 9x3 2x2 + 9x3 + 18x4 + -9x4 = -4x2 + -12x3 + 9x4 + 4x2 + 12x3 + -9x4 Combine like terms: 18x4 + -9x4 = 9x4 2x2 + 9x3 + 9x4 = -4x2 + -12x3 + 9x4 + 4x2 + 12x3 + -9x4 Reorder the terms: 2x2 + 9x3 + 9x4 = -4x2 + 4x2 + -12x3 + 12x3 + 9x4 + -9x4 Combine like terms: -4x2 + 4x2 = 0 2x2 + 9x3 + 9x4 = 0 + -12x3 + 12x3 + 9x4 + -9x4 2x2 + 9x3 + 9x4 = -12x3 + 12x3 + 9x4 + -9x4 Combine like terms: -12x3 + 12x3 = 0 2x2 + 9x3 + 9x4 = 0 + 9x4 + -9x4 2x2 + 9x3 + 9x4 = 9x4 + -9x4 Combine like terms: 9x4 + -9x4 = 0 2x2 + 9x3 + 9x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(2 + 9x + 9x2) = 0 Factor a trinomial. x2((2 + 3x)(1 + 3x)) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 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 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Subproblem 3
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {0, -0.6666666667, -0.3333333333}
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