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Simplifying (5x + 10)(1 + -6x) + -1(3x + 7)(5x + 10) = 0 Reorder the terms: (10 + 5x)(1 + -6x) + -1(3x + 7)(5x + 10) = 0 Multiply (10 + 5x) * (1 + -6x) (10(1 + -6x) + 5x * (1 + -6x)) + -1(3x + 7)(5x + 10) = 0 ((1 * 10 + -6x * 10) + 5x * (1 + -6x)) + -1(3x + 7)(5x + 10) = 0 ((10 + -60x) + 5x * (1 + -6x)) + -1(3x + 7)(5x + 10) = 0 (10 + -60x + (1 * 5x + -6x * 5x)) + -1(3x + 7)(5x + 10) = 0 (10 + -60x + (5x + -30x2)) + -1(3x + 7)(5x + 10) = 0 Combine like terms: -60x + 5x = -55x (10 + -55x + -30x2) + -1(3x + 7)(5x + 10) = 0 Reorder the terms: 10 + -55x + -30x2 + -1(7 + 3x)(5x + 10) = 0 Reorder the terms: 10 + -55x + -30x2 + -1(7 + 3x)(10 + 5x) = 0 Multiply (7 + 3x) * (10 + 5x) 10 + -55x + -30x2 + -1(7(10 + 5x) + 3x * (10 + 5x)) = 0 10 + -55x + -30x2 + -1((10 * 7 + 5x * 7) + 3x * (10 + 5x)) = 0 10 + -55x + -30x2 + -1((70 + 35x) + 3x * (10 + 5x)) = 0 10 + -55x + -30x2 + -1(70 + 35x + (10 * 3x + 5x * 3x)) = 0 10 + -55x + -30x2 + -1(70 + 35x + (30x + 15x2)) = 0 Combine like terms: 35x + 30x = 65x 10 + -55x + -30x2 + -1(70 + 65x + 15x2) = 0 10 + -55x + -30x2 + (70 * -1 + 65x * -1 + 15x2 * -1) = 0 10 + -55x + -30x2 + (-70 + -65x + -15x2) = 0 Reorder the terms: 10 + -70 + -55x + -65x + -30x2 + -15x2 = 0 Combine like terms: 10 + -70 = -60 -60 + -55x + -65x + -30x2 + -15x2 = 0 Combine like terms: -55x + -65x = -120x -60 + -120x + -30x2 + -15x2 = 0 Combine like terms: -30x2 + -15x2 = -45x2 -60 + -120x + -45x2 = 0 Solving -60 + -120x + -45x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-15'. -15(4 + 8x + 3x2) = 0 Factor a trinomial. -15((2 + x)(2 + 3x)) = 0 Ignore the factor -15.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Solution
x = {-2, -0.6666666667}
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