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Simplifying (2x + -1)(x + 3) = (x + 3)(x + 1) Reorder the terms: (-1 + 2x)(x + 3) = (x + 3)(x + 1) Reorder the terms: (-1 + 2x)(3 + x) = (x + 3)(x + 1) Multiply (-1 + 2x) * (3 + x) (-1(3 + x) + 2x * (3 + x)) = (x + 3)(x + 1) ((3 * -1 + x * -1) + 2x * (3 + x)) = (x + 3)(x + 1) ((-3 + -1x) + 2x * (3 + x)) = (x + 3)(x + 1) (-3 + -1x + (3 * 2x + x * 2x)) = (x + 3)(x + 1) (-3 + -1x + (6x + 2x2)) = (x + 3)(x + 1) Combine like terms: -1x + 6x = 5x (-3 + 5x + 2x2) = (x + 3)(x + 1) Reorder the terms: -3 + 5x + 2x2 = (3 + x)(x + 1) Reorder the terms: -3 + 5x + 2x2 = (3 + x)(1 + x) Multiply (3 + x) * (1 + x) -3 + 5x + 2x2 = (3(1 + x) + x(1 + x)) -3 + 5x + 2x2 = ((1 * 3 + x * 3) + x(1 + x)) -3 + 5x + 2x2 = ((3 + 3x) + x(1 + x)) -3 + 5x + 2x2 = (3 + 3x + (1 * x + x * x)) -3 + 5x + 2x2 = (3 + 3x + (1x + x2)) Combine like terms: 3x + 1x = 4x -3 + 5x + 2x2 = (3 + 4x + x2) Solving -3 + 5x + 2x2 = 3 + 4x + x2 Solving for variable 'x'. Reorder the terms: -3 + -3 + 5x + -4x + 2x2 + -1x2 = 3 + 4x + x2 + -3 + -4x + -1x2 Combine like terms: -3 + -3 = -6 -6 + 5x + -4x + 2x2 + -1x2 = 3 + 4x + x2 + -3 + -4x + -1x2 Combine like terms: 5x + -4x = 1x -6 + 1x + 2x2 + -1x2 = 3 + 4x + x2 + -3 + -4x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -6 + 1x + 1x2 = 3 + 4x + x2 + -3 + -4x + -1x2 Reorder the terms: -6 + 1x + 1x2 = 3 + -3 + 4x + -4x + x2 + -1x2 Combine like terms: 3 + -3 = 0 -6 + 1x + 1x2 = 0 + 4x + -4x + x2 + -1x2 -6 + 1x + 1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 -6 + 1x + 1x2 = 0 + x2 + -1x2 -6 + 1x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -6 + 1x + 1x2 = 0 Factor a trinomial. (-3 + -1x)(2 + -1x) = 0Subproblem 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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-3, 2}
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