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Simplifying (2x + 1)(x + 1) = 1 Reorder the terms: (1 + 2x)(x + 1) = 1 Reorder the terms: (1 + 2x)(1 + x) = 1 Multiply (1 + 2x) * (1 + x) (1(1 + x) + 2x * (1 + x)) = 1 ((1 * 1 + x * 1) + 2x * (1 + x)) = 1 ((1 + 1x) + 2x * (1 + x)) = 1 (1 + 1x + (1 * 2x + x * 2x)) = 1 (1 + 1x + (2x + 2x2)) = 1 Combine like terms: 1x + 2x = 3x (1 + 3x + 2x2) = 1 Add '-1' to each side of the equation. 1 + 3x + -1 + 2x2 = 1 + -1 Reorder the terms: 1 + -1 + 3x + 2x2 = 1 + -1 Combine like terms: 1 + -1 = 0 0 + 3x + 2x2 = 1 + -1 3x + 2x2 = 1 + -1 Combine like terms: 1 + -1 = 0 3x + 2x2 = 0 Solving 3x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(3 + 2x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Solution
x = {0, -1.5}
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