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Simplifying (x + 5)(x + -7) + (2x + -5)(x + -1) + 12x + -30 = 0 Reorder the terms: (5 + x)(x + -7) + (2x + -5)(x + -1) + 12x + -30 = 0 Reorder the terms: (5 + x)(-7 + x) + (2x + -5)(x + -1) + 12x + -30 = 0 Multiply (5 + x) * (-7 + x) (5(-7 + x) + x(-7 + x)) + (2x + -5)(x + -1) + 12x + -30 = 0 ((-7 * 5 + x * 5) + x(-7 + x)) + (2x + -5)(x + -1) + 12x + -30 = 0 ((-35 + 5x) + x(-7 + x)) + (2x + -5)(x + -1) + 12x + -30 = 0 (-35 + 5x + (-7 * x + x * x)) + (2x + -5)(x + -1) + 12x + -30 = 0 (-35 + 5x + (-7x + x2)) + (2x + -5)(x + -1) + 12x + -30 = 0 Combine like terms: 5x + -7x = -2x (-35 + -2x + x2) + (2x + -5)(x + -1) + 12x + -30 = 0 Reorder the terms: -35 + -2x + x2 + (-5 + 2x)(x + -1) + 12x + -30 = 0 Reorder the terms: -35 + -2x + x2 + (-5 + 2x)(-1 + x) + 12x + -30 = 0 Multiply (-5 + 2x) * (-1 + x) -35 + -2x + x2 + (-5(-1 + x) + 2x * (-1 + x)) + 12x + -30 = 0 -35 + -2x + x2 + ((-1 * -5 + x * -5) + 2x * (-1 + x)) + 12x + -30 = 0 -35 + -2x + x2 + ((5 + -5x) + 2x * (-1 + x)) + 12x + -30 = 0 -35 + -2x + x2 + (5 + -5x + (-1 * 2x + x * 2x)) + 12x + -30 = 0 -35 + -2x + x2 + (5 + -5x + (-2x + 2x2)) + 12x + -30 = 0 Combine like terms: -5x + -2x = -7x -35 + -2x + x2 + (5 + -7x + 2x2) + 12x + -30 = 0 Reorder the terms: -35 + 5 + -30 + -2x + -7x + 12x + x2 + 2x2 = 0 Combine like terms: -35 + 5 = -30 -30 + -30 + -2x + -7x + 12x + x2 + 2x2 = 0 Combine like terms: -30 + -30 = -60 -60 + -2x + -7x + 12x + x2 + 2x2 = 0 Combine like terms: -2x + -7x = -9x -60 + -9x + 12x + x2 + 2x2 = 0 Combine like terms: -9x + 12x = 3x -60 + 3x + x2 + 2x2 = 0 Combine like terms: x2 + 2x2 = 3x2 -60 + 3x + 3x2 = 0 Solving -60 + 3x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-20 + x + x2) = 0 Factor a trinomial. 3((-5 + -1x)(4 + -1x)) = 0 Ignore the factor 3.Subproblem 1
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 = -5Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-5, 4}
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