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Simplifying (x + 1)(x + 2) + (x + 1) + (x + 3) = 0 Reorder the terms: (1 + x)(x + 2) + (x + 1) + (x + 3) = 0 Reorder the terms: (1 + x)(2 + x) + (x + 1) + (x + 3) = 0 Multiply (1 + x) * (2 + x) (1(2 + x) + x(2 + x)) + (x + 1) + (x + 3) = 0 ((2 * 1 + x * 1) + x(2 + x)) + (x + 1) + (x + 3) = 0 ((2 + 1x) + x(2 + x)) + (x + 1) + (x + 3) = 0 (2 + 1x + (2 * x + x * x)) + (x + 1) + (x + 3) = 0 (2 + 1x + (2x + x2)) + (x + 1) + (x + 3) = 0 Combine like terms: 1x + 2x = 3x (2 + 3x + x2) + (x + 1) + (x + 3) = 0 Reorder the terms: 2 + 3x + x2 + (1 + x) + (x + 3) = 0 Remove parenthesis around (1 + x) 2 + 3x + x2 + 1 + x + (x + 3) = 0 Reorder the terms: 2 + 3x + x2 + 1 + x + (3 + x) = 0 Remove parenthesis around (3 + x) 2 + 3x + x2 + 1 + x + 3 + x = 0 Reorder the terms: 2 + 1 + 3 + 3x + x + x + x2 = 0 Combine like terms: 2 + 1 = 3 3 + 3 + 3x + x + x + x2 = 0 Combine like terms: 3 + 3 = 6 6 + 3x + x + x + x2 = 0 Combine like terms: 3x + x = 4x 6 + 4x + x + x2 = 0 Combine like terms: 4x + x = 5x 6 + 5x + x2 = 0 Solving 6 + 5x + x2 = 0 Solving for variable 'x'. Factor a trinomial. (3 + x)(2 + x) = 0Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-3, -2}
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