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Simplifying (3x + -2)(4x + 7) + -1(2x + 1)(4x + 7) = 0 Reorder the terms: (-2 + 3x)(4x + 7) + -1(2x + 1)(4x + 7) = 0 Reorder the terms: (-2 + 3x)(7 + 4x) + -1(2x + 1)(4x + 7) = 0 Multiply (-2 + 3x) * (7 + 4x) (-2(7 + 4x) + 3x * (7 + 4x)) + -1(2x + 1)(4x + 7) = 0 ((7 * -2 + 4x * -2) + 3x * (7 + 4x)) + -1(2x + 1)(4x + 7) = 0 ((-14 + -8x) + 3x * (7 + 4x)) + -1(2x + 1)(4x + 7) = 0 (-14 + -8x + (7 * 3x + 4x * 3x)) + -1(2x + 1)(4x + 7) = 0 (-14 + -8x + (21x + 12x2)) + -1(2x + 1)(4x + 7) = 0 Combine like terms: -8x + 21x = 13x (-14 + 13x + 12x2) + -1(2x + 1)(4x + 7) = 0 Reorder the terms: -14 + 13x + 12x2 + -1(1 + 2x)(4x + 7) = 0 Reorder the terms: -14 + 13x + 12x2 + -1(1 + 2x)(7 + 4x) = 0 Multiply (1 + 2x) * (7 + 4x) -14 + 13x + 12x2 + -1(1(7 + 4x) + 2x * (7 + 4x)) = 0 -14 + 13x + 12x2 + -1((7 * 1 + 4x * 1) + 2x * (7 + 4x)) = 0 -14 + 13x + 12x2 + -1((7 + 4x) + 2x * (7 + 4x)) = 0 -14 + 13x + 12x2 + -1(7 + 4x + (7 * 2x + 4x * 2x)) = 0 -14 + 13x + 12x2 + -1(7 + 4x + (14x + 8x2)) = 0 Combine like terms: 4x + 14x = 18x -14 + 13x + 12x2 + -1(7 + 18x + 8x2) = 0 -14 + 13x + 12x2 + (7 * -1 + 18x * -1 + 8x2 * -1) = 0 -14 + 13x + 12x2 + (-7 + -18x + -8x2) = 0 Reorder the terms: -14 + -7 + 13x + -18x + 12x2 + -8x2 = 0 Combine like terms: -14 + -7 = -21 -21 + 13x + -18x + 12x2 + -8x2 = 0 Combine like terms: 13x + -18x = -5x -21 + -5x + 12x2 + -8x2 = 0 Combine like terms: 12x2 + -8x2 = 4x2 -21 + -5x + 4x2 = 0 Solving -21 + -5x + 4x2 = 0 Solving for variable 'x'. Factor a trinomial. (-7 + -4x)(3 + -1x) = 0Subproblem 1
Set the factor '(-7 + -4x)' equal to zero and attempt to solve: Simplifying -7 + -4x = 0 Solving -7 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -4x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4x = 0 + 7 -4x = 0 + 7 Combine like terms: 0 + 7 = 7 -4x = 7 Divide each side by '-4'. x = -1.75 Simplifying x = -1.75Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-1.75, 3}
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