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Simplifying (3x + 1)(x + 1) = 1 Reorder the terms: (1 + 3x)(x + 1) = 1 Reorder the terms: (1 + 3x)(1 + x) = 1 Multiply (1 + 3x) * (1 + x) (1(1 + x) + 3x * (1 + x)) = 1 ((1 * 1 + x * 1) + 3x * (1 + x)) = 1 ((1 + 1x) + 3x * (1 + x)) = 1 (1 + 1x + (1 * 3x + x * 3x)) = 1 (1 + 1x + (3x + 3x2)) = 1 Combine like terms: 1x + 3x = 4x (1 + 4x + 3x2) = 1 Add '-1' to each side of the equation. 1 + 4x + -1 + 3x2 = 1 + -1 Reorder the terms: 1 + -1 + 4x + 3x2 = 1 + -1 Combine like terms: 1 + -1 = 0 0 + 4x + 3x2 = 1 + -1 4x + 3x2 = 1 + -1 Combine like terms: 1 + -1 = 0 4x + 3x2 = 0 Solving 4x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(4 + 3x) = 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 '(4 + 3x)' equal to zero and attempt to solve: Simplifying 4 + 3x = 0 Solving 4 + 3x = 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 + 3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x = 0 + -4 3x = 0 + -4 Combine like terms: 0 + -4 = -4 3x = -4 Divide each side by '3'. x = -1.333333333 Simplifying x = -1.333333333Solution
x = {0, -1.333333333}
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