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Simplifying (4x + -6)(2x + 1) + (2x + 1)(4x + 3) = 0 Reorder the terms: (-6 + 4x)(2x + 1) + (2x + 1)(4x + 3) = 0 Reorder the terms: (-6 + 4x)(1 + 2x) + (2x + 1)(4x + 3) = 0 Multiply (-6 + 4x) * (1 + 2x) (-6(1 + 2x) + 4x * (1 + 2x)) + (2x + 1)(4x + 3) = 0 ((1 * -6 + 2x * -6) + 4x * (1 + 2x)) + (2x + 1)(4x + 3) = 0 ((-6 + -12x) + 4x * (1 + 2x)) + (2x + 1)(4x + 3) = 0 (-6 + -12x + (1 * 4x + 2x * 4x)) + (2x + 1)(4x + 3) = 0 (-6 + -12x + (4x + 8x2)) + (2x + 1)(4x + 3) = 0 Combine like terms: -12x + 4x = -8x (-6 + -8x + 8x2) + (2x + 1)(4x + 3) = 0 Reorder the terms: -6 + -8x + 8x2 + (1 + 2x)(4x + 3) = 0 Reorder the terms: -6 + -8x + 8x2 + (1 + 2x)(3 + 4x) = 0 Multiply (1 + 2x) * (3 + 4x) -6 + -8x + 8x2 + (1(3 + 4x) + 2x * (3 + 4x)) = 0 -6 + -8x + 8x2 + ((3 * 1 + 4x * 1) + 2x * (3 + 4x)) = 0 -6 + -8x + 8x2 + ((3 + 4x) + 2x * (3 + 4x)) = 0 -6 + -8x + 8x2 + (3 + 4x + (3 * 2x + 4x * 2x)) = 0 -6 + -8x + 8x2 + (3 + 4x + (6x + 8x2)) = 0 Combine like terms: 4x + 6x = 10x -6 + -8x + 8x2 + (3 + 10x + 8x2) = 0 Reorder the terms: -6 + 3 + -8x + 10x + 8x2 + 8x2 = 0 Combine like terms: -6 + 3 = -3 -3 + -8x + 10x + 8x2 + 8x2 = 0 Combine like terms: -8x + 10x = 2x -3 + 2x + 8x2 + 8x2 = 0 Combine like terms: 8x2 + 8x2 = 16x2 -3 + 2x + 16x2 = 0 Solving -3 + 2x + 16x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -2x)(3 + -8x) = 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 + -8x)' equal to zero and attempt to solve: Simplifying 3 + -8x = 0 Solving 3 + -8x = 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 + -8x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8x = 0 + -3 -8x = 0 + -3 Combine like terms: 0 + -3 = -3 -8x = -3 Divide each side by '-8'. x = 0.375 Simplifying x = 0.375Solution
x = {-0.5, 0.375}
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