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Simplifying (x + 2)(x + 2)(x + -2)(x + -2) = 0 Reorder the terms: (2 + x)(x + 2)(x + -2)(x + -2) = 0 Reorder the terms: (2 + x)(2 + x)(x + -2)(x + -2) = 0 Reorder the terms: (2 + x)(2 + x)(-2 + x)(x + -2) = 0 Reorder the terms: (2 + x)(2 + x)(-2 + x)(-2 + x) = 0 Multiply (2 + x) * (2 + x) (2(2 + x) + x(2 + x))(-2 + x)(-2 + x) = 0 ((2 * 2 + x * 2) + x(2 + x))(-2 + x)(-2 + x) = 0 ((4 + 2x) + x(2 + x))(-2 + x)(-2 + x) = 0 (4 + 2x + (2 * x + x * x))(-2 + x)(-2 + x) = 0 (4 + 2x + (2x + x2))(-2 + x)(-2 + x) = 0 Combine like terms: 2x + 2x = 4x (4 + 4x + x2)(-2 + x)(-2 + x) = 0 Multiply (4 + 4x + x2) * (-2 + x) (4(-2 + x) + 4x * (-2 + x) + x2(-2 + x))(-2 + x) = 0 ((-2 * 4 + x * 4) + 4x * (-2 + x) + x2(-2 + x))(-2 + x) = 0 ((-8 + 4x) + 4x * (-2 + x) + x2(-2 + x))(-2 + x) = 0 (-8 + 4x + (-2 * 4x + x * 4x) + x2(-2 + x))(-2 + x) = 0 (-8 + 4x + (-8x + 4x2) + x2(-2 + x))(-2 + x) = 0 (-8 + 4x + -8x + 4x2 + (-2 * x2 + x * x2))(-2 + x) = 0 (-8 + 4x + -8x + 4x2 + (-2x2 + x3))(-2 + x) = 0 Combine like terms: 4x + -8x = -4x (-8 + -4x + 4x2 + -2x2 + x3)(-2 + x) = 0 Combine like terms: 4x2 + -2x2 = 2x2 (-8 + -4x + 2x2 + x3)(-2 + x) = 0 Multiply (-8 + -4x + 2x2 + x3) * (-2 + x) (-8(-2 + x) + -4x * (-2 + x) + 2x2 * (-2 + x) + x3(-2 + x)) = 0 ((-2 * -8 + x * -8) + -4x * (-2 + x) + 2x2 * (-2 + x) + x3(-2 + x)) = 0 ((16 + -8x) + -4x * (-2 + x) + 2x2 * (-2 + x) + x3(-2 + x)) = 0 (16 + -8x + (-2 * -4x + x * -4x) + 2x2 * (-2 + x) + x3(-2 + x)) = 0 (16 + -8x + (8x + -4x2) + 2x2 * (-2 + x) + x3(-2 + x)) = 0 (16 + -8x + 8x + -4x2 + (-2 * 2x2 + x * 2x2) + x3(-2 + x)) = 0 (16 + -8x + 8x + -4x2 + (-4x2 + 2x3) + x3(-2 + x)) = 0 (16 + -8x + 8x + -4x2 + -4x2 + 2x3 + (-2 * x3 + x * x3)) = 0 (16 + -8x + 8x + -4x2 + -4x2 + 2x3 + (-2x3 + x4)) = 0 Combine like terms: -8x + 8x = 0 (16 + 0 + -4x2 + -4x2 + 2x3 + -2x3 + x4) = 0 (16 + -4x2 + -4x2 + 2x3 + -2x3 + x4) = 0 Combine like terms: -4x2 + -4x2 = -8x2 (16 + -8x2 + 2x3 + -2x3 + x4) = 0 Combine like terms: 2x3 + -2x3 = 0 (16 + -8x2 + 0 + x4) = 0 (16 + -8x2 + x4) = 0 Solving 16 + -8x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (4 + -1x2)(4 + -1x2) = 0 Factor a difference between two squares. ((2 + x)(2 + -1x))(4 + -1x2) = 0 Factor a difference between two squares. ((2 + x)(2 + -1x))(2 + x)(2 + -1x) = 0Subproblem 1
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 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 = 2Subproblem 3
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 4
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, -2, 2}
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