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Simplifying 0 = (4x + -3)(2x + 7) + -1(4x + -3)(6 + -1x) Reorder the terms: 0 = (-3 + 4x)(2x + 7) + -1(4x + -3)(6 + -1x) Reorder the terms: 0 = (-3 + 4x)(7 + 2x) + -1(4x + -3)(6 + -1x) Multiply (-3 + 4x) * (7 + 2x) 0 = (-3(7 + 2x) + 4x * (7 + 2x)) + -1(4x + -3)(6 + -1x) 0 = ((7 * -3 + 2x * -3) + 4x * (7 + 2x)) + -1(4x + -3)(6 + -1x) 0 = ((-21 + -6x) + 4x * (7 + 2x)) + -1(4x + -3)(6 + -1x) 0 = (-21 + -6x + (7 * 4x + 2x * 4x)) + -1(4x + -3)(6 + -1x) 0 = (-21 + -6x + (28x + 8x2)) + -1(4x + -3)(6 + -1x) Combine like terms: -6x + 28x = 22x 0 = (-21 + 22x + 8x2) + -1(4x + -3)(6 + -1x) Reorder the terms: 0 = -21 + 22x + 8x2 + -1(-3 + 4x)(6 + -1x) Multiply (-3 + 4x) * (6 + -1x) 0 = -21 + 22x + 8x2 + -1(-3(6 + -1x) + 4x * (6 + -1x)) 0 = -21 + 22x + 8x2 + -1((6 * -3 + -1x * -3) + 4x * (6 + -1x)) 0 = -21 + 22x + 8x2 + -1((-18 + 3x) + 4x * (6 + -1x)) 0 = -21 + 22x + 8x2 + -1(-18 + 3x + (6 * 4x + -1x * 4x)) 0 = -21 + 22x + 8x2 + -1(-18 + 3x + (24x + -4x2)) Combine like terms: 3x + 24x = 27x 0 = -21 + 22x + 8x2 + -1(-18 + 27x + -4x2) 0 = -21 + 22x + 8x2 + (-18 * -1 + 27x * -1 + -4x2 * -1) 0 = -21 + 22x + 8x2 + (18 + -27x + 4x2) Reorder the terms: 0 = -21 + 18 + 22x + -27x + 8x2 + 4x2 Combine like terms: -21 + 18 = -3 0 = -3 + 22x + -27x + 8x2 + 4x2 Combine like terms: 22x + -27x = -5x 0 = -3 + -5x + 8x2 + 4x2 Combine like terms: 8x2 + 4x2 = 12x2 0 = -3 + -5x + 12x2 Solving 0 = -3 + -5x + 12x2 Solving for variable 'x'. Combine like terms: 0 + 3 = 3 3 + 5x + -12x2 = -3 + -5x + 12x2 + 3 + 5x + -12x2 Reorder the terms: 3 + 5x + -12x2 = -3 + 3 + -5x + 5x + 12x2 + -12x2 Combine like terms: -3 + 3 = 0 3 + 5x + -12x2 = 0 + -5x + 5x + 12x2 + -12x2 3 + 5x + -12x2 = -5x + 5x + 12x2 + -12x2 Combine like terms: -5x + 5x = 0 3 + 5x + -12x2 = 0 + 12x2 + -12x2 3 + 5x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 3 + 5x + -12x2 = 0 Factor a trinomial. (3 + -4x)(1 + 3x) = 0Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 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 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {0.75, -0.3333333333}
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