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Simplifying (x + 1)(2x + -3) = (3x + 3)(x + -2) Reorder the terms: (1 + x)(2x + -3) = (3x + 3)(x + -2) Reorder the terms: (1 + x)(-3 + 2x) = (3x + 3)(x + -2) Multiply (1 + x) * (-3 + 2x) (1(-3 + 2x) + x(-3 + 2x)) = (3x + 3)(x + -2) ((-3 * 1 + 2x * 1) + x(-3 + 2x)) = (3x + 3)(x + -2) ((-3 + 2x) + x(-3 + 2x)) = (3x + 3)(x + -2) (-3 + 2x + (-3 * x + 2x * x)) = (3x + 3)(x + -2) (-3 + 2x + (-3x + 2x2)) = (3x + 3)(x + -2) Combine like terms: 2x + -3x = -1x (-3 + -1x + 2x2) = (3x + 3)(x + -2) Reorder the terms: -3 + -1x + 2x2 = (3 + 3x)(x + -2) Reorder the terms: -3 + -1x + 2x2 = (3 + 3x)(-2 + x) Multiply (3 + 3x) * (-2 + x) -3 + -1x + 2x2 = (3(-2 + x) + 3x * (-2 + x)) -3 + -1x + 2x2 = ((-2 * 3 + x * 3) + 3x * (-2 + x)) -3 + -1x + 2x2 = ((-6 + 3x) + 3x * (-2 + x)) -3 + -1x + 2x2 = (-6 + 3x + (-2 * 3x + x * 3x)) -3 + -1x + 2x2 = (-6 + 3x + (-6x + 3x2)) Combine like terms: 3x + -6x = -3x -3 + -1x + 2x2 = (-6 + -3x + 3x2) Solving -3 + -1x + 2x2 = -6 + -3x + 3x2 Solving for variable 'x'. Reorder the terms: -3 + 6 + -1x + 3x + 2x2 + -3x2 = -6 + -3x + 3x2 + 6 + 3x + -3x2 Combine like terms: -3 + 6 = 3 3 + -1x + 3x + 2x2 + -3x2 = -6 + -3x + 3x2 + 6 + 3x + -3x2 Combine like terms: -1x + 3x = 2x 3 + 2x + 2x2 + -3x2 = -6 + -3x + 3x2 + 6 + 3x + -3x2 Combine like terms: 2x2 + -3x2 = -1x2 3 + 2x + -1x2 = -6 + -3x + 3x2 + 6 + 3x + -3x2 Reorder the terms: 3 + 2x + -1x2 = -6 + 6 + -3x + 3x + 3x2 + -3x2 Combine like terms: -6 + 6 = 0 3 + 2x + -1x2 = 0 + -3x + 3x + 3x2 + -3x2 3 + 2x + -1x2 = -3x + 3x + 3x2 + -3x2 Combine like terms: -3x + 3x = 0 3 + 2x + -1x2 = 0 + 3x2 + -3x2 3 + 2x + -1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 3 + 2x + -1x2 = 0 Factor a trinomial. (3 + -1x)(1 + x) = 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Solution
x = {3, -1}
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