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Simplifying (5x + -7)(2x + -1) + -1(5x + -7)(5x + 8) = 0 Reorder the terms: (-7 + 5x)(2x + -1) + -1(5x + -7)(5x + 8) = 0 Reorder the terms: (-7 + 5x)(-1 + 2x) + -1(5x + -7)(5x + 8) = 0 Multiply (-7 + 5x) * (-1 + 2x) (-7(-1 + 2x) + 5x * (-1 + 2x)) + -1(5x + -7)(5x + 8) = 0 ((-1 * -7 + 2x * -7) + 5x * (-1 + 2x)) + -1(5x + -7)(5x + 8) = 0 ((7 + -14x) + 5x * (-1 + 2x)) + -1(5x + -7)(5x + 8) = 0 (7 + -14x + (-1 * 5x + 2x * 5x)) + -1(5x + -7)(5x + 8) = 0 (7 + -14x + (-5x + 10x2)) + -1(5x + -7)(5x + 8) = 0 Combine like terms: -14x + -5x = -19x (7 + -19x + 10x2) + -1(5x + -7)(5x + 8) = 0 Reorder the terms: 7 + -19x + 10x2 + -1(-7 + 5x)(5x + 8) = 0 Reorder the terms: 7 + -19x + 10x2 + -1(-7 + 5x)(8 + 5x) = 0 Multiply (-7 + 5x) * (8 + 5x) 7 + -19x + 10x2 + -1(-7(8 + 5x) + 5x * (8 + 5x)) = 0 7 + -19x + 10x2 + -1((8 * -7 + 5x * -7) + 5x * (8 + 5x)) = 0 7 + -19x + 10x2 + -1((-56 + -35x) + 5x * (8 + 5x)) = 0 7 + -19x + 10x2 + -1(-56 + -35x + (8 * 5x + 5x * 5x)) = 0 7 + -19x + 10x2 + -1(-56 + -35x + (40x + 25x2)) = 0 Combine like terms: -35x + 40x = 5x 7 + -19x + 10x2 + -1(-56 + 5x + 25x2) = 0 7 + -19x + 10x2 + (-56 * -1 + 5x * -1 + 25x2 * -1) = 0 7 + -19x + 10x2 + (56 + -5x + -25x2) = 0 Reorder the terms: 7 + 56 + -19x + -5x + 10x2 + -25x2 = 0 Combine like terms: 7 + 56 = 63 63 + -19x + -5x + 10x2 + -25x2 = 0 Combine like terms: -19x + -5x = -24x 63 + -24x + 10x2 + -25x2 = 0 Combine like terms: 10x2 + -25x2 = -15x2 63 + -24x + -15x2 = 0 Solving 63 + -24x + -15x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(21 + -8x + -5x2) = 0 Factor a trinomial. 3((7 + -5x)(3 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + -5x)' equal to zero and attempt to solve: Simplifying 7 + -5x = 0 Solving 7 + -5x = 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 + -5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5x = 0 + -7 -5x = 0 + -7 Combine like terms: 0 + -7 = -7 -5x = -7 Divide each side by '-5'. x = 1.4 Simplifying x = 1.4Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {1.4, -3}
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