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