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Simplifying (x2 + 6)(x + -2)(x + 2) = 0 Reorder the terms: (6 + x2)(x + -2)(x + 2) = 0 Reorder the terms: (6 + x2)(-2 + x)(x + 2) = 0 Reorder the terms: (6 + x2)(-2 + x)(2 + x) = 0 Multiply (6 + x2) * (-2 + x) (6(-2 + x) + x2(-2 + x))(2 + x) = 0 ((-2 * 6 + x * 6) + x2(-2 + x))(2 + x) = 0 ((-12 + 6x) + x2(-2 + x))(2 + x) = 0 (-12 + 6x + (-2 * x2 + x * x2))(2 + x) = 0 (-12 + 6x + (-2x2 + x3))(2 + x) = 0 (-12 + 6x + -2x2 + x3)(2 + x) = 0 Multiply (-12 + 6x + -2x2 + x3) * (2 + x) (-12(2 + x) + 6x * (2 + x) + -2x2 * (2 + x) + x3(2 + x)) = 0 ((2 * -12 + x * -12) + 6x * (2 + x) + -2x2 * (2 + x) + x3(2 + x)) = 0 ((-24 + -12x) + 6x * (2 + x) + -2x2 * (2 + x) + x3(2 + x)) = 0 (-24 + -12x + (2 * 6x + x * 6x) + -2x2 * (2 + x) + x3(2 + x)) = 0 (-24 + -12x + (12x + 6x2) + -2x2 * (2 + x) + x3(2 + x)) = 0 (-24 + -12x + 12x + 6x2 + (2 * -2x2 + x * -2x2) + x3(2 + x)) = 0 (-24 + -12x + 12x + 6x2 + (-4x2 + -2x3) + x3(2 + x)) = 0 (-24 + -12x + 12x + 6x2 + -4x2 + -2x3 + (2 * x3 + x * x3)) = 0 (-24 + -12x + 12x + 6x2 + -4x2 + -2x3 + (2x3 + x4)) = 0 Combine like terms: -12x + 12x = 0 (-24 + 0 + 6x2 + -4x2 + -2x3 + 2x3 + x4) = 0 (-24 + 6x2 + -4x2 + -2x3 + 2x3 + x4) = 0 Combine like terms: 6x2 + -4x2 = 2x2 (-24 + 2x2 + -2x3 + 2x3 + x4) = 0 Combine like terms: -2x3 + 2x3 = 0 (-24 + 2x2 + 0 + x4) = 0 (-24 + 2x2 + x4) = 0 Solving -24 + 2x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (-6 + -1x2)(4 + -1x2) = 0 Factor a difference between two squares. (-6 + -1x2)((2 + x)(2 + -1x)) = 0Subproblem 1
Set the factor '(-6 + -1x2)' equal to zero and attempt to solve: Simplifying -6 + -1x2 = 0 Solving -6 + -1x2 = 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 + -1x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x2 = 0 + 6 -1x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -1x2 = 6 Divide each side by '-1'. x2 = -6 Simplifying x2 = -6 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 3
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, 2}
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