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Simplifying (2x + -1)(x + 18) = (x + -6)(x + 3) Reorder the terms: (-1 + 2x)(x + 18) = (x + -6)(x + 3) Reorder the terms: (-1 + 2x)(18 + x) = (x + -6)(x + 3) Multiply (-1 + 2x) * (18 + x) (-1(18 + x) + 2x * (18 + x)) = (x + -6)(x + 3) ((18 * -1 + x * -1) + 2x * (18 + x)) = (x + -6)(x + 3) ((-18 + -1x) + 2x * (18 + x)) = (x + -6)(x + 3) (-18 + -1x + (18 * 2x + x * 2x)) = (x + -6)(x + 3) (-18 + -1x + (36x + 2x2)) = (x + -6)(x + 3) Combine like terms: -1x + 36x = 35x (-18 + 35x + 2x2) = (x + -6)(x + 3) Reorder the terms: -18 + 35x + 2x2 = (-6 + x)(x + 3) Reorder the terms: -18 + 35x + 2x2 = (-6 + x)(3 + x) Multiply (-6 + x) * (3 + x) -18 + 35x + 2x2 = (-6(3 + x) + x(3 + x)) -18 + 35x + 2x2 = ((3 * -6 + x * -6) + x(3 + x)) -18 + 35x + 2x2 = ((-18 + -6x) + x(3 + x)) -18 + 35x + 2x2 = (-18 + -6x + (3 * x + x * x)) -18 + 35x + 2x2 = (-18 + -6x + (3x + x2)) Combine like terms: -6x + 3x = -3x -18 + 35x + 2x2 = (-18 + -3x + x2) Add '18' to each side of the equation. -18 + 35x + 18 + 2x2 = -18 + -3x + 18 + x2 Reorder the terms: -18 + 18 + 35x + 2x2 = -18 + -3x + 18 + x2 Combine like terms: -18 + 18 = 0 0 + 35x + 2x2 = -18 + -3x + 18 + x2 35x + 2x2 = -18 + -3x + 18 + x2 Reorder the terms: 35x + 2x2 = -18 + 18 + -3x + x2 Combine like terms: -18 + 18 = 0 35x + 2x2 = 0 + -3x + x2 35x + 2x2 = -3x + x2 Solving 35x + 2x2 = -3x + x2 Solving for variable 'x'. Reorder the terms: 35x + 3x + 2x2 + -1x2 = -3x + x2 + 3x + -1x2 Combine like terms: 35x + 3x = 38x 38x + 2x2 + -1x2 = -3x + x2 + 3x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 38x + 1x2 = -3x + x2 + 3x + -1x2 Reorder the terms: 38x + 1x2 = -3x + 3x + x2 + -1x2 Combine like terms: -3x + 3x = 0 38x + 1x2 = 0 + x2 + -1x2 38x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 38x + 1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(38 + x) = 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 '(38 + x)' equal to zero and attempt to solve: Simplifying 38 + x = 0 Solving 38 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + x = 0 + -38 Combine like terms: 38 + -38 = 0 0 + x = 0 + -38 x = 0 + -38 Combine like terms: 0 + -38 = -38 x = -38 Simplifying x = -38Solution
x = {0, -38}
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