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Simplifying (3x + -1)(x + 2) = (5x + 1)(x + -2) Reorder the terms: (-1 + 3x)(x + 2) = (5x + 1)(x + -2) Reorder the terms: (-1 + 3x)(2 + x) = (5x + 1)(x + -2) Multiply (-1 + 3x) * (2 + x) (-1(2 + x) + 3x * (2 + x)) = (5x + 1)(x + -2) ((2 * -1 + x * -1) + 3x * (2 + x)) = (5x + 1)(x + -2) ((-2 + -1x) + 3x * (2 + x)) = (5x + 1)(x + -2) (-2 + -1x + (2 * 3x + x * 3x)) = (5x + 1)(x + -2) (-2 + -1x + (6x + 3x2)) = (5x + 1)(x + -2) Combine like terms: -1x + 6x = 5x (-2 + 5x + 3x2) = (5x + 1)(x + -2) Reorder the terms: -2 + 5x + 3x2 = (1 + 5x)(x + -2) Reorder the terms: -2 + 5x + 3x2 = (1 + 5x)(-2 + x) Multiply (1 + 5x) * (-2 + x) -2 + 5x + 3x2 = (1(-2 + x) + 5x * (-2 + x)) -2 + 5x + 3x2 = ((-2 * 1 + x * 1) + 5x * (-2 + x)) -2 + 5x + 3x2 = ((-2 + 1x) + 5x * (-2 + x)) -2 + 5x + 3x2 = (-2 + 1x + (-2 * 5x + x * 5x)) -2 + 5x + 3x2 = (-2 + 1x + (-10x + 5x2)) Combine like terms: 1x + -10x = -9x -2 + 5x + 3x2 = (-2 + -9x + 5x2) Add '2' to each side of the equation. -2 + 5x + 2 + 3x2 = -2 + -9x + 2 + 5x2 Reorder the terms: -2 + 2 + 5x + 3x2 = -2 + -9x + 2 + 5x2 Combine like terms: -2 + 2 = 0 0 + 5x + 3x2 = -2 + -9x + 2 + 5x2 5x + 3x2 = -2 + -9x + 2 + 5x2 Reorder the terms: 5x + 3x2 = -2 + 2 + -9x + 5x2 Combine like terms: -2 + 2 = 0 5x + 3x2 = 0 + -9x + 5x2 5x + 3x2 = -9x + 5x2 Solving 5x + 3x2 = -9x + 5x2 Solving for variable 'x'. Reorder the terms: 5x + 9x + 3x2 + -5x2 = -9x + 5x2 + 9x + -5x2 Combine like terms: 5x + 9x = 14x 14x + 3x2 + -5x2 = -9x + 5x2 + 9x + -5x2 Combine like terms: 3x2 + -5x2 = -2x2 14x + -2x2 = -9x + 5x2 + 9x + -5x2 Reorder the terms: 14x + -2x2 = -9x + 9x + 5x2 + -5x2 Combine like terms: -9x + 9x = 0 14x + -2x2 = 0 + 5x2 + -5x2 14x + -2x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 14x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(7 + -1x) = 0 Ignore the factor 2.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 '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {0, 7}
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