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Simplifying (3x + 1)(2 + -7x) + 6(7x + -2)(5x + 8) = 0 Reorder the terms: (1 + 3x)(2 + -7x) + 6(7x + -2)(5x + 8) = 0 Multiply (1 + 3x) * (2 + -7x) (1(2 + -7x) + 3x * (2 + -7x)) + 6(7x + -2)(5x + 8) = 0 ((2 * 1 + -7x * 1) + 3x * (2 + -7x)) + 6(7x + -2)(5x + 8) = 0 ((2 + -7x) + 3x * (2 + -7x)) + 6(7x + -2)(5x + 8) = 0 (2 + -7x + (2 * 3x + -7x * 3x)) + 6(7x + -2)(5x + 8) = 0 (2 + -7x + (6x + -21x2)) + 6(7x + -2)(5x + 8) = 0 Combine like terms: -7x + 6x = -1x (2 + -1x + -21x2) + 6(7x + -2)(5x + 8) = 0 Reorder the terms: 2 + -1x + -21x2 + 6(-2 + 7x)(5x + 8) = 0 Reorder the terms: 2 + -1x + -21x2 + 6(-2 + 7x)(8 + 5x) = 0 Multiply (-2 + 7x) * (8 + 5x) 2 + -1x + -21x2 + 6(-2(8 + 5x) + 7x * (8 + 5x)) = 0 2 + -1x + -21x2 + 6((8 * -2 + 5x * -2) + 7x * (8 + 5x)) = 0 2 + -1x + -21x2 + 6((-16 + -10x) + 7x * (8 + 5x)) = 0 2 + -1x + -21x2 + 6(-16 + -10x + (8 * 7x + 5x * 7x)) = 0 2 + -1x + -21x2 + 6(-16 + -10x + (56x + 35x2)) = 0 Combine like terms: -10x + 56x = 46x 2 + -1x + -21x2 + 6(-16 + 46x + 35x2) = 0 2 + -1x + -21x2 + (-16 * 6 + 46x * 6 + 35x2 * 6) = 0 2 + -1x + -21x2 + (-96 + 276x + 210x2) = 0 Reorder the terms: 2 + -96 + -1x + 276x + -21x2 + 210x2 = 0 Combine like terms: 2 + -96 = -94 -94 + -1x + 276x + -21x2 + 210x2 = 0 Combine like terms: -1x + 276x = 275x -94 + 275x + -21x2 + 210x2 = 0 Combine like terms: -21x2 + 210x2 = 189x2 -94 + 275x + 189x2 = 0 Solving -94 + 275x + 189x2 = 0 Solving for variable 'x'. Factor a trinomial. (-47 + -27x)(2 + -7x) = 0Subproblem 1
Set the factor '(-47 + -27x)' equal to zero and attempt to solve: Simplifying -47 + -27x = 0 Solving -47 + -27x = 0 Move all terms containing x to the left, all other terms to the right. Add '47' to each side of the equation. -47 + 47 + -27x = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -27x = 0 + 47 -27x = 0 + 47 Combine like terms: 0 + 47 = 47 -27x = 47 Divide each side by '-27'. x = -1.740740741 Simplifying x = -1.740740741Subproblem 2
Set the factor '(2 + -7x)' equal to zero and attempt to solve: Simplifying 2 + -7x = 0 Solving 2 + -7x = 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 + -7x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7x = 0 + -2 -7x = 0 + -2 Combine like terms: 0 + -2 = -2 -7x = -2 Divide each side by '-7'. x = 0.2857142857 Simplifying x = 0.2857142857Solution
x = {-1.740740741, 0.2857142857}
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