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Simplifying (7x + -1)(x + 12) + -1(4x + 18)(7x + -1) = 0 Reorder the terms: (-1 + 7x)(x + 12) + -1(4x + 18)(7x + -1) = 0 Reorder the terms: (-1 + 7x)(12 + x) + -1(4x + 18)(7x + -1) = 0 Multiply (-1 + 7x) * (12 + x) (-1(12 + x) + 7x * (12 + x)) + -1(4x + 18)(7x + -1) = 0 ((12 * -1 + x * -1) + 7x * (12 + x)) + -1(4x + 18)(7x + -1) = 0 ((-12 + -1x) + 7x * (12 + x)) + -1(4x + 18)(7x + -1) = 0 (-12 + -1x + (12 * 7x + x * 7x)) + -1(4x + 18)(7x + -1) = 0 (-12 + -1x + (84x + 7x2)) + -1(4x + 18)(7x + -1) = 0 Combine like terms: -1x + 84x = 83x (-12 + 83x + 7x2) + -1(4x + 18)(7x + -1) = 0 Reorder the terms: -12 + 83x + 7x2 + -1(18 + 4x)(7x + -1) = 0 Reorder the terms: -12 + 83x + 7x2 + -1(18 + 4x)(-1 + 7x) = 0 Multiply (18 + 4x) * (-1 + 7x) -12 + 83x + 7x2 + -1(18(-1 + 7x) + 4x * (-1 + 7x)) = 0 -12 + 83x + 7x2 + -1((-1 * 18 + 7x * 18) + 4x * (-1 + 7x)) = 0 -12 + 83x + 7x2 + -1((-18 + 126x) + 4x * (-1 + 7x)) = 0 -12 + 83x + 7x2 + -1(-18 + 126x + (-1 * 4x + 7x * 4x)) = 0 -12 + 83x + 7x2 + -1(-18 + 126x + (-4x + 28x2)) = 0 Combine like terms: 126x + -4x = 122x -12 + 83x + 7x2 + -1(-18 + 122x + 28x2) = 0 -12 + 83x + 7x2 + (-18 * -1 + 122x * -1 + 28x2 * -1) = 0 -12 + 83x + 7x2 + (18 + -122x + -28x2) = 0 Reorder the terms: -12 + 18 + 83x + -122x + 7x2 + -28x2 = 0 Combine like terms: -12 + 18 = 6 6 + 83x + -122x + 7x2 + -28x2 = 0 Combine like terms: 83x + -122x = -39x 6 + -39x + 7x2 + -28x2 = 0 Combine like terms: 7x2 + -28x2 = -21x2 6 + -39x + -21x2 = 0 Solving 6 + -39x + -21x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(2 + -13x + -7x2) = 0 Factor a trinomial. 3((1 + -7x)(2 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -7x)' equal to zero and attempt to solve: Simplifying 1 + -7x = 0 Solving 1 + -7x = 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 + -7x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7x = 0 + -1 -7x = 0 + -1 Combine like terms: 0 + -1 = -1 -7x = -1 Divide each side by '-7'. x = 0.1428571429 Simplifying x = 0.1428571429Subproblem 2
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 = -2Solution
x = {0.1428571429, -2}
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