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Simplifying -2(x + 1)(2x + 1) = 0 Reorder the terms: -2(1 + x)(2x + 1) = 0 Reorder the terms: -2(1 + x)(1 + 2x) = 0 Multiply (1 + x) * (1 + 2x) -2(1(1 + 2x) + x(1 + 2x)) = 0 -2((1 * 1 + 2x * 1) + x(1 + 2x)) = 0 -2((1 + 2x) + x(1 + 2x)) = 0 -2(1 + 2x + (1 * x + 2x * x)) = 0 -2(1 + 2x + (1x + 2x2)) = 0 Combine like terms: 2x + 1x = 3x -2(1 + 3x + 2x2) = 0 (1 * -2 + 3x * -2 + 2x2 * -2) = 0 (-2 + -6x + -4x2) = 0 Solving -2 + -6x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2'. -2(1 + 3x + 2x2) = 0 Factor a trinomial. -2((1 + x)(1 + 2x)) = 0 Ignore the factor -2.Subproblem 1
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 = -1Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-1, -0.5}
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