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Simplifying (2x + 1)(4x + -3) = (4x + -3) * 3 Reorder the terms: (1 + 2x)(4x + -3) = (4x + -3) * 3 Reorder the terms: (1 + 2x)(-3 + 4x) = (4x + -3) * 3 Multiply (1 + 2x) * (-3 + 4x) (1(-3 + 4x) + 2x * (-3 + 4x)) = (4x + -3) * 3 ((-3 * 1 + 4x * 1) + 2x * (-3 + 4x)) = (4x + -3) * 3 ((-3 + 4x) + 2x * (-3 + 4x)) = (4x + -3) * 3 (-3 + 4x + (-3 * 2x + 4x * 2x)) = (4x + -3) * 3 (-3 + 4x + (-6x + 8x2)) = (4x + -3) * 3 Combine like terms: 4x + -6x = -2x (-3 + -2x + 8x2) = (4x + -3) * 3 Reorder the terms: -3 + -2x + 8x2 = (-3 + 4x) * 3 Reorder the terms for easier multiplication: -3 + -2x + 8x2 = 3(-3 + 4x) -3 + -2x + 8x2 = (-3 * 3 + 4x * 3) -3 + -2x + 8x2 = (-9 + 12x) Solving -3 + -2x + 8x2 = -9 + 12x Solving for variable 'x'. Reorder the terms: -3 + 9 + -2x + -12x + 8x2 = -9 + 12x + 9 + -12x Combine like terms: -3 + 9 = 6 6 + -2x + -12x + 8x2 = -9 + 12x + 9 + -12x Combine like terms: -2x + -12x = -14x 6 + -14x + 8x2 = -9 + 12x + 9 + -12x Reorder the terms: 6 + -14x + 8x2 = -9 + 9 + 12x + -12x Combine like terms: -9 + 9 = 0 6 + -14x + 8x2 = 0 + 12x + -12x 6 + -14x + 8x2 = 12x + -12x Combine like terms: 12x + -12x = 0 6 + -14x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -7x + 4x2) = 0 Factor a trinomial. 2((3 + -4x)(1 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = 0.75Subproblem 2
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 = 1Solution
x = {0.75, 1}
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