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Simplifying (5x + 1)(3x + 1) + (5x + 1)(7x + -6) = 0 Reorder the terms: (1 + 5x)(3x + 1) + (5x + 1)(7x + -6) = 0 Reorder the terms: (1 + 5x)(1 + 3x) + (5x + 1)(7x + -6) = 0 Multiply (1 + 5x) * (1 + 3x) (1(1 + 3x) + 5x * (1 + 3x)) + (5x + 1)(7x + -6) = 0 ((1 * 1 + 3x * 1) + 5x * (1 + 3x)) + (5x + 1)(7x + -6) = 0 ((1 + 3x) + 5x * (1 + 3x)) + (5x + 1)(7x + -6) = 0 (1 + 3x + (1 * 5x + 3x * 5x)) + (5x + 1)(7x + -6) = 0 (1 + 3x + (5x + 15x2)) + (5x + 1)(7x + -6) = 0 Combine like terms: 3x + 5x = 8x (1 + 8x + 15x2) + (5x + 1)(7x + -6) = 0 Reorder the terms: 1 + 8x + 15x2 + (1 + 5x)(7x + -6) = 0 Reorder the terms: 1 + 8x + 15x2 + (1 + 5x)(-6 + 7x) = 0 Multiply (1 + 5x) * (-6 + 7x) 1 + 8x + 15x2 + (1(-6 + 7x) + 5x * (-6 + 7x)) = 0 1 + 8x + 15x2 + ((-6 * 1 + 7x * 1) + 5x * (-6 + 7x)) = 0 1 + 8x + 15x2 + ((-6 + 7x) + 5x * (-6 + 7x)) = 0 1 + 8x + 15x2 + (-6 + 7x + (-6 * 5x + 7x * 5x)) = 0 1 + 8x + 15x2 + (-6 + 7x + (-30x + 35x2)) = 0 Combine like terms: 7x + -30x = -23x 1 + 8x + 15x2 + (-6 + -23x + 35x2) = 0 Reorder the terms: 1 + -6 + 8x + -23x + 15x2 + 35x2 = 0 Combine like terms: 1 + -6 = -5 -5 + 8x + -23x + 15x2 + 35x2 = 0 Combine like terms: 8x + -23x = -15x -5 + -15x + 15x2 + 35x2 = 0 Combine like terms: 15x2 + 35x2 = 50x2 -5 + -15x + 50x2 = 0 Solving -5 + -15x + 50x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-1 + -3x + 10x2) = 0 Factor a trinomial. 5((-1 + -5x)(1 + -2x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-1 + -5x)' equal to zero and attempt to solve: Simplifying -1 + -5x = 0 Solving -1 + -5x = 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 + -5x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5x = 0 + 1 -5x = 0 + 1 Combine like terms: 0 + 1 = 1 -5x = 1 Divide each side by '-5'. x = -0.2 Simplifying x = -0.2Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Solution
x = {-0.2, 0.5}
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