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Simplifying (2x + 1)(4x + -1) = 0 Reorder the terms: (1 + 2x)(4x + -1) = 0 Reorder the terms: (1 + 2x)(-1 + 4x) = 0 Multiply (1 + 2x) * (-1 + 4x) (1(-1 + 4x) + 2x * (-1 + 4x)) = 0 ((-1 * 1 + 4x * 1) + 2x * (-1 + 4x)) = 0 ((-1 + 4x) + 2x * (-1 + 4x)) = 0 (-1 + 4x + (-1 * 2x + 4x * 2x)) = 0 (-1 + 4x + (-2x + 8x2)) = 0 Combine like terms: 4x + -2x = 2x (-1 + 2x + 8x2) = 0 Solving -1 + 2x + 8x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -2x)(1 + -4x) = 0Subproblem 1
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 = -0.5Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Solution
x = {-0.5, 0.25}
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