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Simplifying 3(x + -2)(x + 7) + 2(x + 3)(x + 7) = -10(x + 3)(x + -2) Reorder the terms: 3(-2 + x)(x + 7) + 2(x + 3)(x + 7) = -10(x + 3)(x + -2) Reorder the terms: 3(-2 + x)(7 + x) + 2(x + 3)(x + 7) = -10(x + 3)(x + -2) Multiply (-2 + x) * (7 + x) 3(-2(7 + x) + x(7 + x)) + 2(x + 3)(x + 7) = -10(x + 3)(x + -2) 3((7 * -2 + x * -2) + x(7 + x)) + 2(x + 3)(x + 7) = -10(x + 3)(x + -2) 3((-14 + -2x) + x(7 + x)) + 2(x + 3)(x + 7) = -10(x + 3)(x + -2) 3(-14 + -2x + (7 * x + x * x)) + 2(x + 3)(x + 7) = -10(x + 3)(x + -2) 3(-14 + -2x + (7x + x2)) + 2(x + 3)(x + 7) = -10(x + 3)(x + -2) Combine like terms: -2x + 7x = 5x 3(-14 + 5x + x2) + 2(x + 3)(x + 7) = -10(x + 3)(x + -2) (-14 * 3 + 5x * 3 + x2 * 3) + 2(x + 3)(x + 7) = -10(x + 3)(x + -2) (-42 + 15x + 3x2) + 2(x + 3)(x + 7) = -10(x + 3)(x + -2) Reorder the terms: -42 + 15x + 3x2 + 2(3 + x)(x + 7) = -10(x + 3)(x + -2) Reorder the terms: -42 + 15x + 3x2 + 2(3 + x)(7 + x) = -10(x + 3)(x + -2) Multiply (3 + x) * (7 + x) -42 + 15x + 3x2 + 2(3(7 + x) + x(7 + x)) = -10(x + 3)(x + -2) -42 + 15x + 3x2 + 2((7 * 3 + x * 3) + x(7 + x)) = -10(x + 3)(x + -2) -42 + 15x + 3x2 + 2((21 + 3x) + x(7 + x)) = -10(x + 3)(x + -2) -42 + 15x + 3x2 + 2(21 + 3x + (7 * x + x * x)) = -10(x + 3)(x + -2) -42 + 15x + 3x2 + 2(21 + 3x + (7x + x2)) = -10(x + 3)(x + -2) Combine like terms: 3x + 7x = 10x -42 + 15x + 3x2 + 2(21 + 10x + x2) = -10(x + 3)(x + -2) -42 + 15x + 3x2 + (21 * 2 + 10x * 2 + x2 * 2) = -10(x + 3)(x + -2) -42 + 15x + 3x2 + (42 + 20x + 2x2) = -10(x + 3)(x + -2) Reorder the terms: -42 + 42 + 15x + 20x + 3x2 + 2x2 = -10(x + 3)(x + -2) Combine like terms: -42 + 42 = 0 0 + 15x + 20x + 3x2 + 2x2 = -10(x + 3)(x + -2) 15x + 20x + 3x2 + 2x2 = -10(x + 3)(x + -2) Combine like terms: 15x + 20x = 35x 35x + 3x2 + 2x2 = -10(x + 3)(x + -2) Combine like terms: 3x2 + 2x2 = 5x2 35x + 5x2 = -10(x + 3)(x + -2) Reorder the terms: 35x + 5x2 = -10(3 + x)(x + -2) Reorder the terms: 35x + 5x2 = -10(3 + x)(-2 + x) Multiply (3 + x) * (-2 + x) 35x + 5x2 = -10(3(-2 + x) + x(-2 + x)) 35x + 5x2 = -10((-2 * 3 + x * 3) + x(-2 + x)) 35x + 5x2 = -10((-6 + 3x) + x(-2 + x)) 35x + 5x2 = -10(-6 + 3x + (-2 * x + x * x)) 35x + 5x2 = -10(-6 + 3x + (-2x + x2)) Combine like terms: 3x + -2x = 1x 35x + 5x2 = -10(-6 + 1x + x2) 35x + 5x2 = (-6 * -10 + 1x * -10 + x2 * -10) 35x + 5x2 = (60 + -10x + -10x2) Solving 35x + 5x2 = 60 + -10x + -10x2 Solving for variable 'x'. Reorder the terms: -60 + 35x + 10x + 5x2 + 10x2 = 60 + -10x + -10x2 + -60 + 10x + 10x2 Combine like terms: 35x + 10x = 45x -60 + 45x + 5x2 + 10x2 = 60 + -10x + -10x2 + -60 + 10x + 10x2 Combine like terms: 5x2 + 10x2 = 15x2 -60 + 45x + 15x2 = 60 + -10x + -10x2 + -60 + 10x + 10x2 Reorder the terms: -60 + 45x + 15x2 = 60 + -60 + -10x + 10x + -10x2 + 10x2 Combine like terms: 60 + -60 = 0 -60 + 45x + 15x2 = 0 + -10x + 10x + -10x2 + 10x2 -60 + 45x + 15x2 = -10x + 10x + -10x2 + 10x2 Combine like terms: -10x + 10x = 0 -60 + 45x + 15x2 = 0 + -10x2 + 10x2 -60 + 45x + 15x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 -60 + 45x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(-4 + 3x + x2) = 0 Factor a trinomial. 15((-4 + -1x)(1 + -1x)) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-4, 1}
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