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Simplifying (2x + -3)(4x + 7) + -1(2x + -3)(x + 4) = 0 Reorder the terms: (-3 + 2x)(4x + 7) + -1(2x + -3)(x + 4) = 0 Reorder the terms: (-3 + 2x)(7 + 4x) + -1(2x + -3)(x + 4) = 0 Multiply (-3 + 2x) * (7 + 4x) (-3(7 + 4x) + 2x * (7 + 4x)) + -1(2x + -3)(x + 4) = 0 ((7 * -3 + 4x * -3) + 2x * (7 + 4x)) + -1(2x + -3)(x + 4) = 0 ((-21 + -12x) + 2x * (7 + 4x)) + -1(2x + -3)(x + 4) = 0 (-21 + -12x + (7 * 2x + 4x * 2x)) + -1(2x + -3)(x + 4) = 0 (-21 + -12x + (14x + 8x2)) + -1(2x + -3)(x + 4) = 0 Combine like terms: -12x + 14x = 2x (-21 + 2x + 8x2) + -1(2x + -3)(x + 4) = 0 Reorder the terms: -21 + 2x + 8x2 + -1(-3 + 2x)(x + 4) = 0 Reorder the terms: -21 + 2x + 8x2 + -1(-3 + 2x)(4 + x) = 0 Multiply (-3 + 2x) * (4 + x) -21 + 2x + 8x2 + -1(-3(4 + x) + 2x * (4 + x)) = 0 -21 + 2x + 8x2 + -1((4 * -3 + x * -3) + 2x * (4 + x)) = 0 -21 + 2x + 8x2 + -1((-12 + -3x) + 2x * (4 + x)) = 0 -21 + 2x + 8x2 + -1(-12 + -3x + (4 * 2x + x * 2x)) = 0 -21 + 2x + 8x2 + -1(-12 + -3x + (8x + 2x2)) = 0 Combine like terms: -3x + 8x = 5x -21 + 2x + 8x2 + -1(-12 + 5x + 2x2) = 0 -21 + 2x + 8x2 + (-12 * -1 + 5x * -1 + 2x2 * -1) = 0 -21 + 2x + 8x2 + (12 + -5x + -2x2) = 0 Reorder the terms: -21 + 12 + 2x + -5x + 8x2 + -2x2 = 0 Combine like terms: -21 + 12 = -9 -9 + 2x + -5x + 8x2 + -2x2 = 0 Combine like terms: 2x + -5x = -3x -9 + -3x + 8x2 + -2x2 = 0 Combine like terms: 8x2 + -2x2 = 6x2 -9 + -3x + 6x2 = 0 Solving -9 + -3x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + -1x + 2x2) = 0 Factor a trinomial. 3((-1 + -1x)(3 + -2x)) = 0 Ignore the factor 3.Subproblem 1
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 = -1Subproblem 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 = {-1, 1.5}
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