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Simplifying (3x + 7)(4x + 1) + -1(2 + -3x)(3x + 7) = 0 Reorder the terms: (7 + 3x)(4x + 1) + -1(2 + -3x)(3x + 7) = 0 Reorder the terms: (7 + 3x)(1 + 4x) + -1(2 + -3x)(3x + 7) = 0 Multiply (7 + 3x) * (1 + 4x) (7(1 + 4x) + 3x * (1 + 4x)) + -1(2 + -3x)(3x + 7) = 0 ((1 * 7 + 4x * 7) + 3x * (1 + 4x)) + -1(2 + -3x)(3x + 7) = 0 ((7 + 28x) + 3x * (1 + 4x)) + -1(2 + -3x)(3x + 7) = 0 (7 + 28x + (1 * 3x + 4x * 3x)) + -1(2 + -3x)(3x + 7) = 0 (7 + 28x + (3x + 12x2)) + -1(2 + -3x)(3x + 7) = 0 Combine like terms: 28x + 3x = 31x (7 + 31x + 12x2) + -1(2 + -3x)(3x + 7) = 0 Reorder the terms: 7 + 31x + 12x2 + -1(2 + -3x)(7 + 3x) = 0 Multiply (2 + -3x) * (7 + 3x) 7 + 31x + 12x2 + -1(2(7 + 3x) + -3x * (7 + 3x)) = 0 7 + 31x + 12x2 + -1((7 * 2 + 3x * 2) + -3x * (7 + 3x)) = 0 7 + 31x + 12x2 + -1((14 + 6x) + -3x * (7 + 3x)) = 0 7 + 31x + 12x2 + -1(14 + 6x + (7 * -3x + 3x * -3x)) = 0 7 + 31x + 12x2 + -1(14 + 6x + (-21x + -9x2)) = 0 Combine like terms: 6x + -21x = -15x 7 + 31x + 12x2 + -1(14 + -15x + -9x2) = 0 7 + 31x + 12x2 + (14 * -1 + -15x * -1 + -9x2 * -1) = 0 7 + 31x + 12x2 + (-14 + 15x + 9x2) = 0 Reorder the terms: 7 + -14 + 31x + 15x + 12x2 + 9x2 = 0 Combine like terms: 7 + -14 = -7 -7 + 31x + 15x + 12x2 + 9x2 = 0 Combine like terms: 31x + 15x = 46x -7 + 46x + 12x2 + 9x2 = 0 Combine like terms: 12x2 + 9x2 = 21x2 -7 + 46x + 21x2 = 0 Solving -7 + 46x + 21x2 = 0 Solving for variable 'x'. Factor a trinomial. (-7 + -3x)(1 + -7x) = 0Subproblem 1
Set the factor '(-7 + -3x)' equal to zero and attempt to solve: Simplifying -7 + -3x = 0 Solving -7 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -3x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3x = 0 + 7 -3x = 0 + 7 Combine like terms: 0 + 7 = 7 -3x = 7 Divide each side by '-3'. x = -2.333333333 Simplifying x = -2.333333333Subproblem 2
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 = 0.1428571429Solution
x = {-2.333333333, 0.1428571429}
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