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Simplifying (2x + -3)(4 + 7x) + (2x + -3)(x + 4) = 0 Reorder the terms: (-3 + 2x)(4 + 7x) + (2x + -3)(x + 4) = 0 Multiply (-3 + 2x) * (4 + 7x) (-3(4 + 7x) + 2x * (4 + 7x)) + (2x + -3)(x + 4) = 0 ((4 * -3 + 7x * -3) + 2x * (4 + 7x)) + (2x + -3)(x + 4) = 0 ((-12 + -21x) + 2x * (4 + 7x)) + (2x + -3)(x + 4) = 0 (-12 + -21x + (4 * 2x + 7x * 2x)) + (2x + -3)(x + 4) = 0 (-12 + -21x + (8x + 14x2)) + (2x + -3)(x + 4) = 0 Combine like terms: -21x + 8x = -13x (-12 + -13x + 14x2) + (2x + -3)(x + 4) = 0 Reorder the terms: -12 + -13x + 14x2 + (-3 + 2x)(x + 4) = 0 Reorder the terms: -12 + -13x + 14x2 + (-3 + 2x)(4 + x) = 0 Multiply (-3 + 2x) * (4 + x) -12 + -13x + 14x2 + (-3(4 + x) + 2x * (4 + x)) = 0 -12 + -13x + 14x2 + ((4 * -3 + x * -3) + 2x * (4 + x)) = 0 -12 + -13x + 14x2 + ((-12 + -3x) + 2x * (4 + x)) = 0 -12 + -13x + 14x2 + (-12 + -3x + (4 * 2x + x * 2x)) = 0 -12 + -13x + 14x2 + (-12 + -3x + (8x + 2x2)) = 0 Combine like terms: -3x + 8x = 5x -12 + -13x + 14x2 + (-12 + 5x + 2x2) = 0 Reorder the terms: -12 + -12 + -13x + 5x + 14x2 + 2x2 = 0 Combine like terms: -12 + -12 = -24 -24 + -13x + 5x + 14x2 + 2x2 = 0 Combine like terms: -13x + 5x = -8x -24 + -8x + 14x2 + 2x2 = 0 Combine like terms: 14x2 + 2x2 = 16x2 -24 + -8x + 16x2 = 0 Solving -24 + -8x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(-3 + -1x + 2x2) = 0 Factor a trinomial. 8((-1 + -1x)(3 + -2x)) = 0 Ignore the factor 8.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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