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Simplifying (2x + -3)(4 + 7x) + (2x + -7)(x + 4) = 0 Reorder the terms: (-3 + 2x)(4 + 7x) + (2x + -7)(x + 4) = 0 Multiply (-3 + 2x) * (4 + 7x) (-3(4 + 7x) + 2x * (4 + 7x)) + (2x + -7)(x + 4) = 0 ((4 * -3 + 7x * -3) + 2x * (4 + 7x)) + (2x + -7)(x + 4) = 0 ((-12 + -21x) + 2x * (4 + 7x)) + (2x + -7)(x + 4) = 0 (-12 + -21x + (4 * 2x + 7x * 2x)) + (2x + -7)(x + 4) = 0 (-12 + -21x + (8x + 14x2)) + (2x + -7)(x + 4) = 0 Combine like terms: -21x + 8x = -13x (-12 + -13x + 14x2) + (2x + -7)(x + 4) = 0 Reorder the terms: -12 + -13x + 14x2 + (-7 + 2x)(x + 4) = 0 Reorder the terms: -12 + -13x + 14x2 + (-7 + 2x)(4 + x) = 0 Multiply (-7 + 2x) * (4 + x) -12 + -13x + 14x2 + (-7(4 + x) + 2x * (4 + x)) = 0 -12 + -13x + 14x2 + ((4 * -7 + x * -7) + 2x * (4 + x)) = 0 -12 + -13x + 14x2 + ((-28 + -7x) + 2x * (4 + x)) = 0 -12 + -13x + 14x2 + (-28 + -7x + (4 * 2x + x * 2x)) = 0 -12 + -13x + 14x2 + (-28 + -7x + (8x + 2x2)) = 0 Combine like terms: -7x + 8x = 1x -12 + -13x + 14x2 + (-28 + 1x + 2x2) = 0 Reorder the terms: -12 + -28 + -13x + 1x + 14x2 + 2x2 = 0 Combine like terms: -12 + -28 = -40 -40 + -13x + 1x + 14x2 + 2x2 = 0 Combine like terms: -13x + 1x = -12x -40 + -12x + 14x2 + 2x2 = 0 Combine like terms: 14x2 + 2x2 = 16x2 -40 + -12x + 16x2 = 0 Solving -40 + -12x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + -3x + 4x2) = 0 Factor a trinomial. 4((-5 + -4x)(2 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -4x)' equal to zero and attempt to solve: Simplifying -5 + -4x = 0 Solving -5 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -4x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4x = 0 + 5 -4x = 0 + 5 Combine like terms: 0 + 5 = 5 -4x = 5 Divide each side by '-4'. x = -1.25 Simplifying x = -1.25Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-1.25, 2}
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