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Simplifying (x + -2)(x + 4) + 6(x + 2)(x + -2) = x2 + -4 Reorder the terms: (-2 + x)(x + 4) + 6(x + 2)(x + -2) = x2 + -4 Reorder the terms: (-2 + x)(4 + x) + 6(x + 2)(x + -2) = x2 + -4 Multiply (-2 + x) * (4 + x) (-2(4 + x) + x(4 + x)) + 6(x + 2)(x + -2) = x2 + -4 ((4 * -2 + x * -2) + x(4 + x)) + 6(x + 2)(x + -2) = x2 + -4 ((-8 + -2x) + x(4 + x)) + 6(x + 2)(x + -2) = x2 + -4 (-8 + -2x + (4 * x + x * x)) + 6(x + 2)(x + -2) = x2 + -4 (-8 + -2x + (4x + x2)) + 6(x + 2)(x + -2) = x2 + -4 Combine like terms: -2x + 4x = 2x (-8 + 2x + x2) + 6(x + 2)(x + -2) = x2 + -4 Reorder the terms: -8 + 2x + x2 + 6(2 + x)(x + -2) = x2 + -4 Reorder the terms: -8 + 2x + x2 + 6(2 + x)(-2 + x) = x2 + -4 Multiply (2 + x) * (-2 + x) -8 + 2x + x2 + 6(2(-2 + x) + x(-2 + x)) = x2 + -4 -8 + 2x + x2 + 6((-2 * 2 + x * 2) + x(-2 + x)) = x2 + -4 -8 + 2x + x2 + 6((-4 + 2x) + x(-2 + x)) = x2 + -4 -8 + 2x + x2 + 6(-4 + 2x + (-2 * x + x * x)) = x2 + -4 -8 + 2x + x2 + 6(-4 + 2x + (-2x + x2)) = x2 + -4 Combine like terms: 2x + -2x = 0 -8 + 2x + x2 + 6(-4 + 0 + x2) = x2 + -4 -8 + 2x + x2 + 6(-4 + x2) = x2 + -4 -8 + 2x + x2 + (-4 * 6 + x2 * 6) = x2 + -4 -8 + 2x + x2 + (-24 + 6x2) = x2 + -4 Reorder the terms: -8 + -24 + 2x + x2 + 6x2 = x2 + -4 Combine like terms: -8 + -24 = -32 -32 + 2x + x2 + 6x2 = x2 + -4 Combine like terms: x2 + 6x2 = 7x2 -32 + 2x + 7x2 = x2 + -4 Reorder the terms: -32 + 2x + 7x2 = -4 + x2 Solving -32 + 2x + 7x2 = -4 + x2 Solving for variable 'x'. Reorder the terms: -32 + 4 + 2x + 7x2 + -1x2 = -4 + x2 + 4 + -1x2 Combine like terms: -32 + 4 = -28 -28 + 2x + 7x2 + -1x2 = -4 + x2 + 4 + -1x2 Combine like terms: 7x2 + -1x2 = 6x2 -28 + 2x + 6x2 = -4 + x2 + 4 + -1x2 Reorder the terms: -28 + 2x + 6x2 = -4 + 4 + x2 + -1x2 Combine like terms: -4 + 4 = 0 -28 + 2x + 6x2 = 0 + x2 + -1x2 -28 + 2x + 6x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -28 + 2x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + x + 3x2) = 0 Factor a trinomial. 2((-7 + -3x)(2 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -3x)' equal to zero and attempt to solve: Simplifying -7 + -3x = 0 Solving -7 + -3x = 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 + -3x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3x = 0 + 7 -3x = 0 + 7 Combine like terms: 0 + 7 = 7 -3x = 7 Divide each side by '-3'. x = -2.333333333 Simplifying x = -2.333333333Subproblem 2
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 = 2Solution
x = {-2.333333333, 2}
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