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Simplifying (x + 4)(x + 4)(x + -4)(x + -4) = 0 Reorder the terms: (4 + x)(x + 4)(x + -4)(x + -4) = 0 Reorder the terms: (4 + x)(4 + x)(x + -4)(x + -4) = 0 Reorder the terms: (4 + x)(4 + x)(-4 + x)(x + -4) = 0 Reorder the terms: (4 + x)(4 + x)(-4 + x)(-4 + x) = 0 Multiply (4 + x) * (4 + x) (4(4 + x) + x(4 + x))(-4 + x)(-4 + x) = 0 ((4 * 4 + x * 4) + x(4 + x))(-4 + x)(-4 + x) = 0 ((16 + 4x) + x(4 + x))(-4 + x)(-4 + x) = 0 (16 + 4x + (4 * x + x * x))(-4 + x)(-4 + x) = 0 (16 + 4x + (4x + x2))(-4 + x)(-4 + x) = 0 Combine like terms: 4x + 4x = 8x (16 + 8x + x2)(-4 + x)(-4 + x) = 0 Multiply (16 + 8x + x2) * (-4 + x) (16(-4 + x) + 8x * (-4 + x) + x2(-4 + x))(-4 + x) = 0 ((-4 * 16 + x * 16) + 8x * (-4 + x) + x2(-4 + x))(-4 + x) = 0 ((-64 + 16x) + 8x * (-4 + x) + x2(-4 + x))(-4 + x) = 0 (-64 + 16x + (-4 * 8x + x * 8x) + x2(-4 + x))(-4 + x) = 0 (-64 + 16x + (-32x + 8x2) + x2(-4 + x))(-4 + x) = 0 (-64 + 16x + -32x + 8x2 + (-4 * x2 + x * x2))(-4 + x) = 0 (-64 + 16x + -32x + 8x2 + (-4x2 + x3))(-4 + x) = 0 Combine like terms: 16x + -32x = -16x (-64 + -16x + 8x2 + -4x2 + x3)(-4 + x) = 0 Combine like terms: 8x2 + -4x2 = 4x2 (-64 + -16x + 4x2 + x3)(-4 + x) = 0 Multiply (-64 + -16x + 4x2 + x3) * (-4 + x) (-64(-4 + x) + -16x * (-4 + x) + 4x2 * (-4 + x) + x3(-4 + x)) = 0 ((-4 * -64 + x * -64) + -16x * (-4 + x) + 4x2 * (-4 + x) + x3(-4 + x)) = 0 ((256 + -64x) + -16x * (-4 + x) + 4x2 * (-4 + x) + x3(-4 + x)) = 0 (256 + -64x + (-4 * -16x + x * -16x) + 4x2 * (-4 + x) + x3(-4 + x)) = 0 (256 + -64x + (64x + -16x2) + 4x2 * (-4 + x) + x3(-4 + x)) = 0 (256 + -64x + 64x + -16x2 + (-4 * 4x2 + x * 4x2) + x3(-4 + x)) = 0 (256 + -64x + 64x + -16x2 + (-16x2 + 4x3) + x3(-4 + x)) = 0 (256 + -64x + 64x + -16x2 + -16x2 + 4x3 + (-4 * x3 + x * x3)) = 0 (256 + -64x + 64x + -16x2 + -16x2 + 4x3 + (-4x3 + x4)) = 0 Combine like terms: -64x + 64x = 0 (256 + 0 + -16x2 + -16x2 + 4x3 + -4x3 + x4) = 0 (256 + -16x2 + -16x2 + 4x3 + -4x3 + x4) = 0 Combine like terms: -16x2 + -16x2 = -32x2 (256 + -32x2 + 4x3 + -4x3 + x4) = 0 Combine like terms: 4x3 + -4x3 = 0 (256 + -32x2 + 0 + x4) = 0 (256 + -32x2 + x4) = 0 Solving 256 + -32x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (16 + -1x2)(16 + -1x2) = 0 Factor a difference between two squares. ((4 + x)(4 + -1x))(16 + -1x2) = 0 Factor a difference between two squares. ((4 + x)(4 + -1x))(4 + x)(4 + -1x) = 0Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 3
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 4
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-4, 4, -4, 4}
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