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Simplifying 2(x + 4)(x + -4) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x) Reorder the terms: 2(4 + x)(x + -4) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x) Reorder the terms: 2(4 + x)(-4 + x) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x) Multiply (4 + x) * (-4 + x) 2(4(-4 + x) + x(-4 + x)) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x) 2((-4 * 4 + x * 4) + x(-4 + x)) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x) 2((-16 + 4x) + x(-4 + x)) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x) 2(-16 + 4x + (-4 * x + x * x)) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x) 2(-16 + 4x + (-4x + x2)) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x) Combine like terms: 4x + -4x = 0 2(-16 + 0 + x2) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x) 2(-16 + x2) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x) (-16 * 2 + x2 * 2) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x) (-32 + 2x2) + -2(x + -3) = 6(2x + -5) + -2(10 + -1x) Reorder the terms: -32 + 2x2 + -2(-3 + x) = 6(2x + -5) + -2(10 + -1x) -32 + 2x2 + (-3 * -2 + x * -2) = 6(2x + -5) + -2(10 + -1x) -32 + 2x2 + (6 + -2x) = 6(2x + -5) + -2(10 + -1x) Reorder the terms: -32 + 6 + -2x + 2x2 = 6(2x + -5) + -2(10 + -1x) Combine like terms: -32 + 6 = -26 -26 + -2x + 2x2 = 6(2x + -5) + -2(10 + -1x) Reorder the terms: -26 + -2x + 2x2 = 6(-5 + 2x) + -2(10 + -1x) -26 + -2x + 2x2 = (-5 * 6 + 2x * 6) + -2(10 + -1x) -26 + -2x + 2x2 = (-30 + 12x) + -2(10 + -1x) -26 + -2x + 2x2 = -30 + 12x + (10 * -2 + -1x * -2) -26 + -2x + 2x2 = -30 + 12x + (-20 + 2x) Reorder the terms: -26 + -2x + 2x2 = -30 + -20 + 12x + 2x Combine like terms: -30 + -20 = -50 -26 + -2x + 2x2 = -50 + 12x + 2x Combine like terms: 12x + 2x = 14x -26 + -2x + 2x2 = -50 + 14x Solving -26 + -2x + 2x2 = -50 + 14x Solving for variable 'x'. Reorder the terms: -26 + 50 + -2x + -14x + 2x2 = -50 + 14x + 50 + -14x Combine like terms: -26 + 50 = 24 24 + -2x + -14x + 2x2 = -50 + 14x + 50 + -14x Combine like terms: -2x + -14x = -16x 24 + -16x + 2x2 = -50 + 14x + 50 + -14x Reorder the terms: 24 + -16x + 2x2 = -50 + 50 + 14x + -14x Combine like terms: -50 + 50 = 0 24 + -16x + 2x2 = 0 + 14x + -14x 24 + -16x + 2x2 = 14x + -14x Combine like terms: 14x + -14x = 0 24 + -16x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -8x + x2) = 0 Factor a trinomial. 2((2 + -1x)(6 + -1x)) = 0 Ignore the factor 2.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 '(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 = 6Solution
x = {2, 6}
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