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Simplifying (x + 1)(x + -3) = (x + 1)(2x + 3) Reorder the terms: (1 + x)(x + -3) = (x + 1)(2x + 3) Reorder the terms: (1 + x)(-3 + x) = (x + 1)(2x + 3) Multiply (1 + x) * (-3 + x) (1(-3 + x) + x(-3 + x)) = (x + 1)(2x + 3) ((-3 * 1 + x * 1) + x(-3 + x)) = (x + 1)(2x + 3) ((-3 + 1x) + x(-3 + x)) = (x + 1)(2x + 3) (-3 + 1x + (-3 * x + x * x)) = (x + 1)(2x + 3) (-3 + 1x + (-3x + x2)) = (x + 1)(2x + 3) Combine like terms: 1x + -3x = -2x (-3 + -2x + x2) = (x + 1)(2x + 3) Reorder the terms: -3 + -2x + x2 = (1 + x)(2x + 3) Reorder the terms: -3 + -2x + x2 = (1 + x)(3 + 2x) Multiply (1 + x) * (3 + 2x) -3 + -2x + x2 = (1(3 + 2x) + x(3 + 2x)) -3 + -2x + x2 = ((3 * 1 + 2x * 1) + x(3 + 2x)) -3 + -2x + x2 = ((3 + 2x) + x(3 + 2x)) -3 + -2x + x2 = (3 + 2x + (3 * x + 2x * x)) -3 + -2x + x2 = (3 + 2x + (3x + 2x2)) Combine like terms: 2x + 3x = 5x -3 + -2x + x2 = (3 + 5x + 2x2) Solving -3 + -2x + x2 = 3 + 5x + 2x2 Solving for variable 'x'. Reorder the terms: -3 + -3 + -2x + -5x + x2 + -2x2 = 3 + 5x + 2x2 + -3 + -5x + -2x2 Combine like terms: -3 + -3 = -6 -6 + -2x + -5x + x2 + -2x2 = 3 + 5x + 2x2 + -3 + -5x + -2x2 Combine like terms: -2x + -5x = -7x -6 + -7x + x2 + -2x2 = 3 + 5x + 2x2 + -3 + -5x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -6 + -7x + -1x2 = 3 + 5x + 2x2 + -3 + -5x + -2x2 Reorder the terms: -6 + -7x + -1x2 = 3 + -3 + 5x + -5x + 2x2 + -2x2 Combine like terms: 3 + -3 = 0 -6 + -7x + -1x2 = 0 + 5x + -5x + 2x2 + -2x2 -6 + -7x + -1x2 = 5x + -5x + 2x2 + -2x2 Combine like terms: 5x + -5x = 0 -6 + -7x + -1x2 = 0 + 2x2 + -2x2 -6 + -7x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -6 + -7x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 7x + x2) = 0 Factor a trinomial. -1((6 + x)(1 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 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 = {-6, -1}
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