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Simplifying 3(x2 + 2x + -9) = 33 + -1x(x + 2) Reorder the terms: 3(-9 + 2x + x2) = 33 + -1x(x + 2) (-9 * 3 + 2x * 3 + x2 * 3) = 33 + -1x(x + 2) (-27 + 6x + 3x2) = 33 + -1x(x + 2) Reorder the terms: -27 + 6x + 3x2 = 33 + -1x(2 + x) -27 + 6x + 3x2 = 33 + (2 * -1x + x * -1x) -27 + 6x + 3x2 = 33 + (-2x + -1x2) Solving -27 + 6x + 3x2 = 33 + -2x + -1x2 Solving for variable 'x'. Reorder the terms: -27 + -33 + 6x + 2x + 3x2 + x2 = 33 + -2x + -1x2 + -33 + 2x + x2 Combine like terms: -27 + -33 = -60 -60 + 6x + 2x + 3x2 + x2 = 33 + -2x + -1x2 + -33 + 2x + x2 Combine like terms: 6x + 2x = 8x -60 + 8x + 3x2 + x2 = 33 + -2x + -1x2 + -33 + 2x + x2 Combine like terms: 3x2 + x2 = 4x2 -60 + 8x + 4x2 = 33 + -2x + -1x2 + -33 + 2x + x2 Reorder the terms: -60 + 8x + 4x2 = 33 + -33 + -2x + 2x + -1x2 + x2 Combine like terms: 33 + -33 = 0 -60 + 8x + 4x2 = 0 + -2x + 2x + -1x2 + x2 -60 + 8x + 4x2 = -2x + 2x + -1x2 + x2 Combine like terms: -2x + 2x = 0 -60 + 8x + 4x2 = 0 + -1x2 + x2 -60 + 8x + 4x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -60 + 8x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + 2x + x2) = 0 Factor a trinomial. 4((-5 + -1x)(3 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 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 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 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 = 3Solution
x = {-5, 3}
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