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Simplifying 3(x + 5)(x + -5) + -12 = 5(3x + 3) + -60 Reorder the terms: 3(5 + x)(x + -5) + -12 = 5(3x + 3) + -60 Reorder the terms: 3(5 + x)(-5 + x) + -12 = 5(3x + 3) + -60 Multiply (5 + x) * (-5 + x) 3(5(-5 + x) + x(-5 + x)) + -12 = 5(3x + 3) + -60 3((-5 * 5 + x * 5) + x(-5 + x)) + -12 = 5(3x + 3) + -60 3((-25 + 5x) + x(-5 + x)) + -12 = 5(3x + 3) + -60 3(-25 + 5x + (-5 * x + x * x)) + -12 = 5(3x + 3) + -60 3(-25 + 5x + (-5x + x2)) + -12 = 5(3x + 3) + -60 Combine like terms: 5x + -5x = 0 3(-25 + 0 + x2) + -12 = 5(3x + 3) + -60 3(-25 + x2) + -12 = 5(3x + 3) + -60 (-25 * 3 + x2 * 3) + -12 = 5(3x + 3) + -60 (-75 + 3x2) + -12 = 5(3x + 3) + -60 Reorder the terms: -75 + -12 + 3x2 = 5(3x + 3) + -60 Combine like terms: -75 + -12 = -87 -87 + 3x2 = 5(3x + 3) + -60 Reorder the terms: -87 + 3x2 = 5(3 + 3x) + -60 -87 + 3x2 = (3 * 5 + 3x * 5) + -60 -87 + 3x2 = (15 + 15x) + -60 Reorder the terms: -87 + 3x2 = 15 + -60 + 15x Combine like terms: 15 + -60 = -45 -87 + 3x2 = -45 + 15x Solving -87 + 3x2 = -45 + 15x Solving for variable 'x'. Reorder the terms: -87 + 45 + -15x + 3x2 = -45 + 15x + 45 + -15x Combine like terms: -87 + 45 = -42 -42 + -15x + 3x2 = -45 + 15x + 45 + -15x Reorder the terms: -42 + -15x + 3x2 = -45 + 45 + 15x + -15x Combine like terms: -45 + 45 = 0 -42 + -15x + 3x2 = 0 + 15x + -15x -42 + -15x + 3x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -42 + -15x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-14 + -5x + x2) = 0 Factor a trinomial. 3((-2 + -1x)(7 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 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 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-2, 7}
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