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Simplifying (2x + -1)(x + 3) = (x + -3)(x + 1) Reorder the terms: (-1 + 2x)(x + 3) = (x + -3)(x + 1) Reorder the terms: (-1 + 2x)(3 + x) = (x + -3)(x + 1) Multiply (-1 + 2x) * (3 + x) (-1(3 + x) + 2x * (3 + x)) = (x + -3)(x + 1) ((3 * -1 + x * -1) + 2x * (3 + x)) = (x + -3)(x + 1) ((-3 + -1x) + 2x * (3 + x)) = (x + -3)(x + 1) (-3 + -1x + (3 * 2x + x * 2x)) = (x + -3)(x + 1) (-3 + -1x + (6x + 2x2)) = (x + -3)(x + 1) Combine like terms: -1x + 6x = 5x (-3 + 5x + 2x2) = (x + -3)(x + 1) Reorder the terms: -3 + 5x + 2x2 = (-3 + x)(x + 1) Reorder the terms: -3 + 5x + 2x2 = (-3 + x)(1 + x) Multiply (-3 + x) * (1 + x) -3 + 5x + 2x2 = (-3(1 + x) + x(1 + x)) -3 + 5x + 2x2 = ((1 * -3 + x * -3) + x(1 + x)) -3 + 5x + 2x2 = ((-3 + -3x) + x(1 + x)) -3 + 5x + 2x2 = (-3 + -3x + (1 * x + x * x)) -3 + 5x + 2x2 = (-3 + -3x + (1x + x2)) Combine like terms: -3x + 1x = -2x -3 + 5x + 2x2 = (-3 + -2x + x2) Add '3' to each side of the equation. -3 + 5x + 3 + 2x2 = -3 + -2x + 3 + x2 Reorder the terms: -3 + 3 + 5x + 2x2 = -3 + -2x + 3 + x2 Combine like terms: -3 + 3 = 0 0 + 5x + 2x2 = -3 + -2x + 3 + x2 5x + 2x2 = -3 + -2x + 3 + x2 Reorder the terms: 5x + 2x2 = -3 + 3 + -2x + x2 Combine like terms: -3 + 3 = 0 5x + 2x2 = 0 + -2x + x2 5x + 2x2 = -2x + x2 Solving 5x + 2x2 = -2x + x2 Solving for variable 'x'. Reorder the terms: 5x + 2x + 2x2 + -1x2 = -2x + x2 + 2x + -1x2 Combine like terms: 5x + 2x = 7x 7x + 2x2 + -1x2 = -2x + x2 + 2x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 7x + 1x2 = -2x + x2 + 2x + -1x2 Reorder the terms: 7x + 1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 7x + 1x2 = 0 + x2 + -1x2 7x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 7x + 1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(7 + 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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Solution
x = {0, -7}
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