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Simplifying (x + 5)(x + -3) + (x + 7)(x + -3) = 0 Reorder the terms: (5 + x)(x + -3) + (x + 7)(x + -3) = 0 Reorder the terms: (5 + x)(-3 + x) + (x + 7)(x + -3) = 0 Multiply (5 + x) * (-3 + x) (5(-3 + x) + x(-3 + x)) + (x + 7)(x + -3) = 0 ((-3 * 5 + x * 5) + x(-3 + x)) + (x + 7)(x + -3) = 0 ((-15 + 5x) + x(-3 + x)) + (x + 7)(x + -3) = 0 (-15 + 5x + (-3 * x + x * x)) + (x + 7)(x + -3) = 0 (-15 + 5x + (-3x + x2)) + (x + 7)(x + -3) = 0 Combine like terms: 5x + -3x = 2x (-15 + 2x + x2) + (x + 7)(x + -3) = 0 Reorder the terms: -15 + 2x + x2 + (7 + x)(x + -3) = 0 Reorder the terms: -15 + 2x + x2 + (7 + x)(-3 + x) = 0 Multiply (7 + x) * (-3 + x) -15 + 2x + x2 + (7(-3 + x) + x(-3 + x)) = 0 -15 + 2x + x2 + ((-3 * 7 + x * 7) + x(-3 + x)) = 0 -15 + 2x + x2 + ((-21 + 7x) + x(-3 + x)) = 0 -15 + 2x + x2 + (-21 + 7x + (-3 * x + x * x)) = 0 -15 + 2x + x2 + (-21 + 7x + (-3x + x2)) = 0 Combine like terms: 7x + -3x = 4x -15 + 2x + x2 + (-21 + 4x + x2) = 0 Reorder the terms: -15 + -21 + 2x + 4x + x2 + x2 = 0 Combine like terms: -15 + -21 = -36 -36 + 2x + 4x + x2 + x2 = 0 Combine like terms: 2x + 4x = 6x -36 + 6x + x2 + x2 = 0 Combine like terms: x2 + x2 = 2x2 -36 + 6x + 2x2 = 0 Solving -36 + 6x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-18 + 3x + x2) = 0 Factor a trinomial. 2((-6 + -1x)(3 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-6, 3}
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