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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. (-1 + -4x)(3 + -2x) = 0Subproblem 1
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 = -0.25Subproblem 2
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 = 1.5Solution
x = {-0.25, 1.5}
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