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Simplifying (2x + 1)(4x + -3) = (4x + -3) * 2 Reorder the terms: (1 + 2x)(4x + -3) = (4x + -3) * 2 Reorder the terms: (1 + 2x)(-3 + 4x) = (4x + -3) * 2 Multiply (1 + 2x) * (-3 + 4x) (1(-3 + 4x) + 2x * (-3 + 4x)) = (4x + -3) * 2 ((-3 * 1 + 4x * 1) + 2x * (-3 + 4x)) = (4x + -3) * 2 ((-3 + 4x) + 2x * (-3 + 4x)) = (4x + -3) * 2 (-3 + 4x + (-3 * 2x + 4x * 2x)) = (4x + -3) * 2 (-3 + 4x + (-6x + 8x2)) = (4x + -3) * 2 Combine like terms: 4x + -6x = -2x (-3 + -2x + 8x2) = (4x + -3) * 2 Reorder the terms: -3 + -2x + 8x2 = (-3 + 4x) * 2 Reorder the terms for easier multiplication: -3 + -2x + 8x2 = 2(-3 + 4x) -3 + -2x + 8x2 = (-3 * 2 + 4x * 2) -3 + -2x + 8x2 = (-6 + 8x) Solving -3 + -2x + 8x2 = -6 + 8x Solving for variable 'x'. Reorder the terms: -3 + 6 + -2x + -8x + 8x2 = -6 + 8x + 6 + -8x Combine like terms: -3 + 6 = 3 3 + -2x + -8x + 8x2 = -6 + 8x + 6 + -8x Combine like terms: -2x + -8x = -10x 3 + -10x + 8x2 = -6 + 8x + 6 + -8x Reorder the terms: 3 + -10x + 8x2 = -6 + 6 + 8x + -8x Combine like terms: -6 + 6 = 0 3 + -10x + 8x2 = 0 + 8x + -8x 3 + -10x + 8x2 = 8x + -8x Combine like terms: 8x + -8x = 0 3 + -10x + 8x2 = 0 Factor a trinomial. (1 + -2x)(3 + -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 '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Solution
x = {0.5, 0.75}
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