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Simplifying (2x + 3)(4x + -1) = 0 Reorder the terms: (3 + 2x)(4x + -1) = 0 Reorder the terms: (3 + 2x)(-1 + 4x) = 0 Multiply (3 + 2x) * (-1 + 4x) (3(-1 + 4x) + 2x * (-1 + 4x)) = 0 ((-1 * 3 + 4x * 3) + 2x * (-1 + 4x)) = 0 ((-3 + 12x) + 2x * (-1 + 4x)) = 0 (-3 + 12x + (-1 * 2x + 4x * 2x)) = 0 (-3 + 12x + (-2x + 8x2)) = 0 Combine like terms: 12x + -2x = 10x (-3 + 10x + 8x2) = 0 Solving -3 + 10x + 8x2 = 0 Solving for variable 'x'. Factor a trinomial. (-3 + -2x)(1 + -4x) = 0Subproblem 1
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 = -1.5Subproblem 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 = {-1.5, 0.25}
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