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Simplifying (x + 3)(2x + -1) = (x + 3)(2 + -1x) Reorder the terms: (3 + x)(2x + -1) = (x + 3)(2 + -1x) Reorder the terms: (3 + x)(-1 + 2x) = (x + 3)(2 + -1x) Multiply (3 + x) * (-1 + 2x) (3(-1 + 2x) + x(-1 + 2x)) = (x + 3)(2 + -1x) ((-1 * 3 + 2x * 3) + x(-1 + 2x)) = (x + 3)(2 + -1x) ((-3 + 6x) + x(-1 + 2x)) = (x + 3)(2 + -1x) (-3 + 6x + (-1 * x + 2x * x)) = (x + 3)(2 + -1x) (-3 + 6x + (-1x + 2x2)) = (x + 3)(2 + -1x) Combine like terms: 6x + -1x = 5x (-3 + 5x + 2x2) = (x + 3)(2 + -1x) Reorder the terms: -3 + 5x + 2x2 = (3 + x)(2 + -1x) Multiply (3 + x) * (2 + -1x) -3 + 5x + 2x2 = (3(2 + -1x) + x(2 + -1x)) -3 + 5x + 2x2 = ((2 * 3 + -1x * 3) + x(2 + -1x)) -3 + 5x + 2x2 = ((6 + -3x) + x(2 + -1x)) -3 + 5x + 2x2 = (6 + -3x + (2 * x + -1x * x)) -3 + 5x + 2x2 = (6 + -3x + (2x + -1x2)) Combine like terms: -3x + 2x = -1x -3 + 5x + 2x2 = (6 + -1x + -1x2) Solving -3 + 5x + 2x2 = 6 + -1x + -1x2 Solving for variable 'x'. Reorder the terms: -3 + -6 + 5x + x + 2x2 + x2 = 6 + -1x + -1x2 + -6 + x + x2 Combine like terms: -3 + -6 = -9 -9 + 5x + x + 2x2 + x2 = 6 + -1x + -1x2 + -6 + x + x2 Combine like terms: 5x + x = 6x -9 + 6x + 2x2 + x2 = 6 + -1x + -1x2 + -6 + x + x2 Combine like terms: 2x2 + x2 = 3x2 -9 + 6x + 3x2 = 6 + -1x + -1x2 + -6 + x + x2 Reorder the terms: -9 + 6x + 3x2 = 6 + -6 + -1x + x + -1x2 + x2 Combine like terms: 6 + -6 = 0 -9 + 6x + 3x2 = 0 + -1x + x + -1x2 + x2 -9 + 6x + 3x2 = -1x + x + -1x2 + x2 Combine like terms: -1x + x = 0 -9 + 6x + 3x2 = 0 + -1x2 + x2 -9 + 6x + 3x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -9 + 6x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + 2x + x2) = 0 Factor a trinomial. 3((-3 + -1x)(1 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 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 = {-3, 1}
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