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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 Reorder the terms: 2 + 3x + x2 + (1 + x)(3 + x) = 0 Multiply (1 + x) * (3 + x) 2 + 3x + x2 + (1(3 + x) + x(3 + x)) = 0 2 + 3x + x2 + ((3 * 1 + x * 1) + x(3 + x)) = 0 2 + 3x + x2 + ((3 + 1x) + x(3 + x)) = 0 2 + 3x + x2 + (3 + 1x + (3 * x + x * x)) = 0 2 + 3x + x2 + (3 + 1x + (3x + x2)) = 0 Combine like terms: 1x + 3x = 4x 2 + 3x + x2 + (3 + 4x + x2) = 0 Reorder the terms: 2 + 3 + 3x + 4x + x2 + x2 = 0 Combine like terms: 2 + 3 = 5 5 + 3x + 4x + x2 + x2 = 0 Combine like terms: 3x + 4x = 7x 5 + 7x + x2 + x2 = 0 Combine like terms: x2 + x2 = 2x2 5 + 7x + 2x2 = 0 Solving 5 + 7x + 2x2 = 0 Solving for variable 'x'. Factor a trinomial. (5 + 2x)(1 + x) = 0Subproblem 1
Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Subproblem 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 = {-2.5, -1}
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