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Simplifying (x + 9) * x(4x + -3) = (x + -6) * x(1 + -3x) Reorder the terms: (9 + x) * x(4x + -3) = (x + -6) * x(1 + -3x) Reorder the terms: (9 + x) * x(-3 + 4x) = (x + -6) * x(1 + -3x) Reorder the terms for easier multiplication: x(9 + x)(-3 + 4x) = (x + -6) * x(1 + -3x) Multiply (9 + x) * (-3 + 4x) x(9(-3 + 4x) + x(-3 + 4x)) = (x + -6) * x(1 + -3x) x((-3 * 9 + 4x * 9) + x(-3 + 4x)) = (x + -6) * x(1 + -3x) x((-27 + 36x) + x(-3 + 4x)) = (x + -6) * x(1 + -3x) x(-27 + 36x + (-3 * x + 4x * x)) = (x + -6) * x(1 + -3x) x(-27 + 36x + (-3x + 4x2)) = (x + -6) * x(1 + -3x) Combine like terms: 36x + -3x = 33x x(-27 + 33x + 4x2) = (x + -6) * x(1 + -3x) (-27 * x + 33x * x + 4x2 * x) = (x + -6) * x(1 + -3x) (-27x + 33x2 + 4x3) = (x + -6) * x(1 + -3x) Reorder the terms: -27x + 33x2 + 4x3 = (-6 + x) * x(1 + -3x) Reorder the terms for easier multiplication: -27x + 33x2 + 4x3 = x(-6 + x)(1 + -3x) Multiply (-6 + x) * (1 + -3x) -27x + 33x2 + 4x3 = x(-6(1 + -3x) + x(1 + -3x)) -27x + 33x2 + 4x3 = x((1 * -6 + -3x * -6) + x(1 + -3x)) -27x + 33x2 + 4x3 = x((-6 + 18x) + x(1 + -3x)) -27x + 33x2 + 4x3 = x(-6 + 18x + (1 * x + -3x * x)) -27x + 33x2 + 4x3 = x(-6 + 18x + (1x + -3x2)) Combine like terms: 18x + 1x = 19x -27x + 33x2 + 4x3 = x(-6 + 19x + -3x2) -27x + 33x2 + 4x3 = (-6 * x + 19x * x + -3x2 * x) -27x + 33x2 + 4x3 = (-6x + 19x2 + -3x3) Solving -27x + 33x2 + 4x3 = -6x + 19x2 + -3x3 Solving for variable 'x'. Reorder the terms: -27x + 6x + 33x2 + -19x2 + 4x3 + 3x3 = -6x + 19x2 + -3x3 + 6x + -19x2 + 3x3 Combine like terms: -27x + 6x = -21x -21x + 33x2 + -19x2 + 4x3 + 3x3 = -6x + 19x2 + -3x3 + 6x + -19x2 + 3x3 Combine like terms: 33x2 + -19x2 = 14x2 -21x + 14x2 + 4x3 + 3x3 = -6x + 19x2 + -3x3 + 6x + -19x2 + 3x3 Combine like terms: 4x3 + 3x3 = 7x3 -21x + 14x2 + 7x3 = -6x + 19x2 + -3x3 + 6x + -19x2 + 3x3 Reorder the terms: -21x + 14x2 + 7x3 = -6x + 6x + 19x2 + -19x2 + -3x3 + 3x3 Combine like terms: -6x + 6x = 0 -21x + 14x2 + 7x3 = 0 + 19x2 + -19x2 + -3x3 + 3x3 -21x + 14x2 + 7x3 = 19x2 + -19x2 + -3x3 + 3x3 Combine like terms: 19x2 + -19x2 = 0 -21x + 14x2 + 7x3 = 0 + -3x3 + 3x3 -21x + 14x2 + 7x3 = -3x3 + 3x3 Combine like terms: -3x3 + 3x3 = 0 -21x + 14x2 + 7x3 = 0 Factor out the Greatest Common Factor (GCF), '7x'. 7x(-3 + 2x + x2) = 0 Factor a trinomial. 7x((-3 + -1x)(1 + -1x)) = 0 Ignore the factor 7.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 + -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 = -3Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0, -3, 1}
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