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Simplifying x2 + 2x + -3 = 3(x + -1)(x + 9) Reorder the terms: -3 + 2x + x2 = 3(x + -1)(x + 9) Reorder the terms: -3 + 2x + x2 = 3(-1 + x)(x + 9) Reorder the terms: -3 + 2x + x2 = 3(-1 + x)(9 + x) Multiply (-1 + x) * (9 + x) -3 + 2x + x2 = 3(-1(9 + x) + x(9 + x)) -3 + 2x + x2 = 3((9 * -1 + x * -1) + x(9 + x)) -3 + 2x + x2 = 3((-9 + -1x) + x(9 + x)) -3 + 2x + x2 = 3(-9 + -1x + (9 * x + x * x)) -3 + 2x + x2 = 3(-9 + -1x + (9x + x2)) Combine like terms: -1x + 9x = 8x -3 + 2x + x2 = 3(-9 + 8x + x2) -3 + 2x + x2 = (-9 * 3 + 8x * 3 + x2 * 3) -3 + 2x + x2 = (-27 + 24x + 3x2) Solving -3 + 2x + x2 = -27 + 24x + 3x2 Solving for variable 'x'. Reorder the terms: -3 + 27 + 2x + -24x + x2 + -3x2 = -27 + 24x + 3x2 + 27 + -24x + -3x2 Combine like terms: -3 + 27 = 24 24 + 2x + -24x + x2 + -3x2 = -27 + 24x + 3x2 + 27 + -24x + -3x2 Combine like terms: 2x + -24x = -22x 24 + -22x + x2 + -3x2 = -27 + 24x + 3x2 + 27 + -24x + -3x2 Combine like terms: x2 + -3x2 = -2x2 24 + -22x + -2x2 = -27 + 24x + 3x2 + 27 + -24x + -3x2 Reorder the terms: 24 + -22x + -2x2 = -27 + 27 + 24x + -24x + 3x2 + -3x2 Combine like terms: -27 + 27 = 0 24 + -22x + -2x2 = 0 + 24x + -24x + 3x2 + -3x2 24 + -22x + -2x2 = 24x + -24x + 3x2 + -3x2 Combine like terms: 24x + -24x = 0 24 + -22x + -2x2 = 0 + 3x2 + -3x2 24 + -22x + -2x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 24 + -22x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -11x + -1x2) = 0 Factor a trinomial. 2((1 + -1x)(12 + x)) = 0 Ignore the factor 2.Subproblem 1
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 = 1Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Simplifying x = -12Solution
x = {1, -12}
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