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Simplifying (2x + 1)(-3x + 2) = -5x + 2 Reorder the terms: (1 + 2x)(-3x + 2) = -5x + 2 Reorder the terms: (1 + 2x)(2 + -3x) = -5x + 2 Multiply (1 + 2x) * (2 + -3x) (1(2 + -3x) + 2x * (2 + -3x)) = -5x + 2 ((2 * 1 + -3x * 1) + 2x * (2 + -3x)) = -5x + 2 ((2 + -3x) + 2x * (2 + -3x)) = -5x + 2 (2 + -3x + (2 * 2x + -3x * 2x)) = -5x + 2 (2 + -3x + (4x + -6x2)) = -5x + 2 Combine like terms: -3x + 4x = 1x (2 + 1x + -6x2) = -5x + 2 Reorder the terms: 2 + 1x + -6x2 = 2 + -5x Add '-2' to each side of the equation. 2 + 1x + -2 + -6x2 = 2 + -2 + -5x Reorder the terms: 2 + -2 + 1x + -6x2 = 2 + -2 + -5x Combine like terms: 2 + -2 = 0 0 + 1x + -6x2 = 2 + -2 + -5x 1x + -6x2 = 2 + -2 + -5x Combine like terms: 2 + -2 = 0 1x + -6x2 = 0 + -5x 1x + -6x2 = -5x Solving 1x + -6x2 = -5x Solving for variable 'x'. Reorder the terms: 1x + 5x + -6x2 = -5x + 5x Combine like terms: 1x + 5x = 6x 6x + -6x2 = -5x + 5x Combine like terms: -5x + 5x = 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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