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Simplifying (3x + 1)(-2x + 2) = 0 Reorder the terms: (1 + 3x)(-2x + 2) = 0 Reorder the terms: (1 + 3x)(2 + -2x) = 0 Multiply (1 + 3x) * (2 + -2x) (1(2 + -2x) + 3x * (2 + -2x)) = 0 ((2 * 1 + -2x * 1) + 3x * (2 + -2x)) = 0 ((2 + -2x) + 3x * (2 + -2x)) = 0 (2 + -2x + (2 * 3x + -2x * 3x)) = 0 (2 + -2x + (6x + -6x2)) = 0 Combine like terms: -2x + 6x = 4x (2 + 4x + -6x2) = 0 Solving 2 + 4x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 2x + -3x2) = 0 Factor a trinomial. 2((1 + -1x)(1 + 3x)) = 0 Ignore the factor 2.Subproblem 1
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 = 1Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {1, -0.3333333333}
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