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Simplifying (x4n + 4y2n)(x4n + -4y2n) = 0 Multiply (nx4 + 4ny2) * (nx4 + -4ny2) (nx4(nx4 + -4ny2) + 4ny2 * (nx4 + -4ny2)) = 0 ((nx4 * nx4 + -4ny2 * nx4) + 4ny2 * (nx4 + -4ny2)) = 0 Reorder the terms: ((-4n2x4y2 + n2x8) + 4ny2 * (nx4 + -4ny2)) = 0 ((-4n2x4y2 + n2x8) + 4ny2 * (nx4 + -4ny2)) = 0 (-4n2x4y2 + n2x8 + (nx4 * 4ny2 + -4ny2 * 4ny2)) = 0 (-4n2x4y2 + n2x8 + (4n2x4y2 + -16n2y4)) = 0 Reorder the terms: (-4n2x4y2 + 4n2x4y2 + n2x8 + -16n2y4) = 0 Combine like terms: -4n2x4y2 + 4n2x4y2 = 0 (0 + n2x8 + -16n2y4) = 0 (n2x8 + -16n2y4) = 0 Solving n2x8 + -16n2y4 = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'n2'. n2(x8 + -16y4) = 0 Factor a difference between two squares. n2((x4 + 4y2)(x4 + -4y2)) = 0 Factor a difference between two squares. n2((x4 + 4y2)((x2 + 2y)(x2 + -2y))) = 0Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve: Simplifying n2 = 0 Solving n2 = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n2 = 0 Take the square root of each side: n = {0}Subproblem 2
Set the factor '(x4 + 4y2)' equal to zero and attempt to solve: Simplifying x4 + 4y2 = 0 Solving x4 + 4y2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-1x4' to each side of the equation. x4 + -1x4 + 4y2 = 0 + -1x4 Combine like terms: x4 + -1x4 = 0 0 + 4y2 = 0 + -1x4 4y2 = 0 + -1x4 Remove the zero: 4y2 = -1x4 Add '-4y2' to each side of the equation. 4y2 + -4y2 = -1x4 + -4y2 Combine like terms: 4y2 + -4y2 = 0 0 = -1x4 + -4y2 Simplifying 0 = -1x4 + -4y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(x2 + 2y)' equal to zero and attempt to solve: Simplifying x2 + 2y = 0 Solving x2 + 2y = 0 Move all terms containing n to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + -1x2 + 2y = 0 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 2y = 0 + -1x2 2y = 0 + -1x2 Remove the zero: 2y = -1x2 Add '-2y' to each side of the equation. 2y + -2y = -1x2 + -2y Combine like terms: 2y + -2y = 0 0 = -1x2 + -2y Simplifying 0 = -1x2 + -2y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 4
Set the factor '(x2 + -2y)' equal to zero and attempt to solve: Simplifying x2 + -2y = 0 Solving x2 + -2y = 0 Move all terms containing n to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + -1x2 + -2y = 0 + -1x2 Combine like terms: x2 + -1x2 = 0 0 + -2y = 0 + -1x2 -2y = 0 + -1x2 Remove the zero: -2y = -1x2 Add '2y' to each side of the equation. -2y + 2y = -1x2 + 2y Combine like terms: -2y + 2y = 0 0 = -1x2 + 2y Simplifying 0 = -1x2 + 2y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
n = {0}
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