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Simplifying (x3 + 4x2)(x3 + -4x2) = 0 Reorder the terms: (4x2 + x3)(x3 + -4x2) = 0 Reorder the terms: (4x2 + x3)(-4x2 + x3) = 0 Multiply (4x2 + x3) * (-4x2 + x3) (4x2 * (-4x2 + x3) + x3(-4x2 + x3)) = 0 ((-4x2 * 4x2 + x3 * 4x2) + x3(-4x2 + x3)) = 0 ((-16x4 + 4x5) + x3(-4x2 + x3)) = 0 (-16x4 + 4x5 + (-4x2 * x3 + x3 * x3)) = 0 (-16x4 + 4x5 + (-4x5 + x6)) = 0 Combine like terms: 4x5 + -4x5 = 0 (-16x4 + 0 + x6) = 0 (-16x4 + x6) = 0 Solving -16x4 + x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x4'. x4(-16 + x2) = 0 Factor a difference between two squares. x4((4 + x)(-4 + x)) = 0Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve: Simplifying x4 = 0 Solving x4 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x4 = 0 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 '(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 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 = 4Solution
x = {-4, 4}
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