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Simplifying (3x + 1)(x + -7) + (x + -3)(3x + 1) = 0 Reorder the terms: (1 + 3x)(x + -7) + (x + -3)(3x + 1) = 0 Reorder the terms: (1 + 3x)(-7 + x) + (x + -3)(3x + 1) = 0 Multiply (1 + 3x) * (-7 + x) (1(-7 + x) + 3x * (-7 + x)) + (x + -3)(3x + 1) = 0 ((-7 * 1 + x * 1) + 3x * (-7 + x)) + (x + -3)(3x + 1) = 0 ((-7 + 1x) + 3x * (-7 + x)) + (x + -3)(3x + 1) = 0 (-7 + 1x + (-7 * 3x + x * 3x)) + (x + -3)(3x + 1) = 0 (-7 + 1x + (-21x + 3x2)) + (x + -3)(3x + 1) = 0 Combine like terms: 1x + -21x = -20x (-7 + -20x + 3x2) + (x + -3)(3x + 1) = 0 Reorder the terms: -7 + -20x + 3x2 + (-3 + x)(3x + 1) = 0 Reorder the terms: -7 + -20x + 3x2 + (-3 + x)(1 + 3x) = 0 Multiply (-3 + x) * (1 + 3x) -7 + -20x + 3x2 + (-3(1 + 3x) + x(1 + 3x)) = 0 -7 + -20x + 3x2 + ((1 * -3 + 3x * -3) + x(1 + 3x)) = 0 -7 + -20x + 3x2 + ((-3 + -9x) + x(1 + 3x)) = 0 -7 + -20x + 3x2 + (-3 + -9x + (1 * x + 3x * x)) = 0 -7 + -20x + 3x2 + (-3 + -9x + (1x + 3x2)) = 0 Combine like terms: -9x + 1x = -8x -7 + -20x + 3x2 + (-3 + -8x + 3x2) = 0 Reorder the terms: -7 + -3 + -20x + -8x + 3x2 + 3x2 = 0 Combine like terms: -7 + -3 = -10 -10 + -20x + -8x + 3x2 + 3x2 = 0 Combine like terms: -20x + -8x = -28x -10 + -28x + 3x2 + 3x2 = 0 Combine like terms: 3x2 + 3x2 = 6x2 -10 + -28x + 6x2 = 0 Solving -10 + -28x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -14x + 3x2) = 0 Factor a trinomial. 2((-1 + -3x)(5 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 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 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-0.3333333333, 5}
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