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Simplifying 3(3x + -1) + -4(2x + -1) = (3x + -1)(2x + -1) Reorder the terms: 3(-1 + 3x) + -4(2x + -1) = (3x + -1)(2x + -1) (-1 * 3 + 3x * 3) + -4(2x + -1) = (3x + -1)(2x + -1) (-3 + 9x) + -4(2x + -1) = (3x + -1)(2x + -1) Reorder the terms: -3 + 9x + -4(-1 + 2x) = (3x + -1)(2x + -1) -3 + 9x + (-1 * -4 + 2x * -4) = (3x + -1)(2x + -1) -3 + 9x + (4 + -8x) = (3x + -1)(2x + -1) Reorder the terms: -3 + 4 + 9x + -8x = (3x + -1)(2x + -1) Combine like terms: -3 + 4 = 1 1 + 9x + -8x = (3x + -1)(2x + -1) Combine like terms: 9x + -8x = 1x 1 + 1x = (3x + -1)(2x + -1) Reorder the terms: 1 + 1x = (-1 + 3x)(2x + -1) Reorder the terms: 1 + 1x = (-1 + 3x)(-1 + 2x) Multiply (-1 + 3x) * (-1 + 2x) 1 + 1x = (-1(-1 + 2x) + 3x * (-1 + 2x)) 1 + 1x = ((-1 * -1 + 2x * -1) + 3x * (-1 + 2x)) 1 + 1x = ((1 + -2x) + 3x * (-1 + 2x)) 1 + 1x = (1 + -2x + (-1 * 3x + 2x * 3x)) 1 + 1x = (1 + -2x + (-3x + 6x2)) Combine like terms: -2x + -3x = -5x 1 + 1x = (1 + -5x + 6x2) Add '-1' to each side of the equation. 1 + -1 + 1x = 1 + -5x + -1 + 6x2 Combine like terms: 1 + -1 = 0 0 + 1x = 1 + -5x + -1 + 6x2 1x = 1 + -5x + -1 + 6x2 Reorder the terms: 1x = 1 + -1 + -5x + 6x2 Combine like terms: 1 + -1 = 0 1x = 0 + -5x + 6x2 1x = -5x + 6x2 Solving 1x = -5x + 6x2 Solving for variable 'x'. Combine like terms: 1x + 5x = 6x 6x + -6x2 = -5x + 6x2 + 5x + -6x2 Reorder the terms: 6x + -6x2 = -5x + 5x + 6x2 + -6x2 Combine like terms: -5x + 5x = 0 6x + -6x2 = 0 + 6x2 + -6x2 6x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 6x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '6x'. 6x(1 + -1x) = 0 Ignore the factor 6.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 '(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 = 1Solution
x = {0, 1}
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