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