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Simplifying (14)(10)(2x + 5)(7x + 6) + -1(14)(10)(2x + 5)(5x + 1) = (x + -1)(2x + 5)(14)(10) Reorder the terms: 14 * 10(5 + 2x)(7x + 6) + -1(14)(10)(2x + 5)(5x + 1) = (x + -1)(2x + 5)(14)(10) Reorder the terms: 14 * 10(5 + 2x)(6 + 7x) + -1(14)(10)(2x + 5)(5x + 1) = (x + -1)(2x + 5)(14)(10) Multiply 14 * 10 140(5 + 2x)(6 + 7x) + -1(14)(10)(2x + 5)(5x + 1) = (x + -1)(2x + 5)(14)(10) Multiply (5 + 2x) * (6 + 7x) 140(5(6 + 7x) + 2x * (6 + 7x)) + -1(14)(10)(2x + 5)(5x + 1) = (x + -1)(2x + 5)(14)(10) 140((6 * 5 + 7x * 5) + 2x * (6 + 7x)) + -1(14)(10)(2x + 5)(5x + 1) = (x + -1)(2x + 5)(14)(10) 140((30 + 35x) + 2x * (6 + 7x)) + -1(14)(10)(2x + 5)(5x + 1) = (x + -1)(2x + 5)(14)(10) 140(30 + 35x + (6 * 2x + 7x * 2x)) + -1(14)(10)(2x + 5)(5x + 1) = (x + -1)(2x + 5)(14)(10) 140(30 + 35x + (12x + 14x2)) + -1(14)(10)(2x + 5)(5x + 1) = (x + -1)(2x + 5)(14)(10) Combine like terms: 35x + 12x = 47x 140(30 + 47x + 14x2) + -1(14)(10)(2x + 5)(5x + 1) = (x + -1)(2x + 5)(14)(10) (30 * 140 + 47x * 140 + 14x2 * 140) + -1(14)(10)(2x + 5)(5x + 1) = (x + -1)(2x + 5)(14)(10) (4200 + 6580x + 1960x2) + -1(14)(10)(2x + 5)(5x + 1) = (x + -1)(2x + 5)(14)(10) Reorder the terms: 4200 + 6580x + 1960x2 + -1 * 14 * 10(5 + 2x)(5x + 1) = (x + -1)(2x + 5)(14)(10) Reorder the terms: 4200 + 6580x + 1960x2 + -1 * 14 * 10(5 + 2x)(1 + 5x) = (x + -1)(2x + 5)(14)(10) Multiply -1 * 14 4200 + 6580x + 1960x2 + -14 * 10(5 + 2x)(1 + 5x) = (x + -1)(2x + 5)(14)(10) Multiply -14 * 10 4200 + 6580x + 1960x2 + -140(5 + 2x)(1 + 5x) = (x + -1)(2x + 5)(14)(10) Multiply (5 + 2x) * (1 + 5x) 4200 + 6580x + 1960x2 + -140(5(1 + 5x) + 2x * (1 + 5x)) = (x + -1)(2x + 5)(14)(10) 4200 + 6580x + 1960x2 + -140((1 * 5 + 5x * 5) + 2x * (1 + 5x)) = (x + -1)(2x + 5)(14)(10) 4200 + 6580x + 1960x2 + -140((5 + 25x) + 2x * (1 + 5x)) = (x + -1)(2x + 5)(14)(10) 4200 + 6580x + 1960x2 + -140(5 + 25x + (1 * 2x + 5x * 2x)) = (x + -1)(2x + 5)(14)(10) 4200 + 6580x + 1960x2 + -140(5 + 25x + (2x + 10x2)) = (x + -1)(2x + 5)(14)(10) Combine like terms: 25x + 2x = 27x 4200 + 6580x + 1960x2 + -140(5 + 27x + 10x2) = (x + -1)(2x + 5)(14)(10) 4200 + 6580x + 1960x2 + (5 * -140 + 27x * -140 + 10x2 * -140) = (x + -1)(2x + 5)(14)(10) 4200 + 6580x + 1960x2 + (-700 + -3780x + -1400x2) = (x + -1)(2x + 5)(14)(10) Reorder the terms: 4200 + -700 + 6580x + -3780x + 1960x2 + -1400x2 = (x + -1)(2x + 5)(14)(10) Combine like terms: 4200 + -700 = 3500 3500 + 6580x + -3780x + 1960x2 + -1400x2 = (x + -1)(2x + 5)(14)(10) Combine like terms: 6580x + -3780x = 2800x 3500 + 2800x + 1960x2 + -1400x2 = (x + -1)(2x + 5)(14)(10) Combine like terms: 1960x2 + -1400x2 = 560x2 3500 + 2800x + 560x2 = (x + -1)(2x + 5)(14)(10) Reorder the terms: 3500 + 2800x + 560x2 = (-1 + x)(2x + 5)(14)(10) Reorder the terms: 3500 + 2800x + 560x2 = (-1 + x)(5 + 2x)(14)(10) Reorder the terms for easier multiplication: 3500 + 2800x + 560x2 = 14 * 10(-1 + x)(5 + 2x) Multiply 14 * 10 3500 + 2800x + 560x2 = 140(-1 + x)(5 + 2x) Multiply (-1 + x) * (5 + 2x) 3500 + 2800x + 560x2 = 140(-1(5 + 2x) + x(5 + 2x)) 3500 + 2800x + 560x2 = 140((5 * -1 + 2x * -1) + x(5 + 2x)) 3500 + 2800x + 560x2 = 140((-5 + -2x) + x(5 + 2x)) 3500 + 2800x + 560x2 = 140(-5 + -2x + (5 * x + 2x * x)) 3500 + 2800x + 560x2 = 140(-5 + -2x + (5x + 2x2)) Combine like terms: -2x + 5x = 3x 3500 + 2800x + 560x2 = 140(-5 + 3x + 2x2) 3500 + 2800x + 560x2 = (-5 * 140 + 3x * 140 + 2x2 * 140) 3500 + 2800x + 560x2 = (-700 + 420x + 280x2) Solving 3500 + 2800x + 560x2 = -700 + 420x + 280x2 Solving for variable 'x'. Reorder the terms: 3500 + 700 + 2800x + -420x + 560x2 + -280x2 = -700 + 420x + 280x2 + 700 + -420x + -280x2 Combine like terms: 3500 + 700 = 4200 4200 + 2800x + -420x + 560x2 + -280x2 = -700 + 420x + 280x2 + 700 + -420x + -280x2 Combine like terms: 2800x + -420x = 2380x 4200 + 2380x + 560x2 + -280x2 = -700 + 420x + 280x2 + 700 + -420x + -280x2 Combine like terms: 560x2 + -280x2 = 280x2 4200 + 2380x + 280x2 = -700 + 420x + 280x2 + 700 + -420x + -280x2 Reorder the terms: 4200 + 2380x + 280x2 = -700 + 700 + 420x + -420x + 280x2 + -280x2 Combine like terms: -700 + 700 = 0 4200 + 2380x + 280x2 = 0 + 420x + -420x + 280x2 + -280x2 4200 + 2380x + 280x2 = 420x + -420x + 280x2 + -280x2 Combine like terms: 420x + -420x = 0 4200 + 2380x + 280x2 = 0 + 280x2 + -280x2 4200 + 2380x + 280x2 = 280x2 + -280x2 Combine like terms: 280x2 + -280x2 = 0 4200 + 2380x + 280x2 = 0 Factor out the Greatest Common Factor (GCF), '140'. 140(30 + 17x + 2x2) = 0 Factor a trinomial. 140((6 + x)(5 + 2x)) = 0 Ignore the factor 140.Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 2
Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 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 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Solution
x = {-6, -2.5}
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