9aq^4-9an^4=0

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Solution for 9aq^4-9an^4=0 equation:


Simplifying
9aq4 + -9an4 = 0

Reorder the terms:
-9an4 + 9aq4 = 0

Solving
-9an4 + 9aq4 = 0

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Factor out the Greatest Common Factor (GCF), '9a'.
9a(-1n4 + q4) = 0

Factor a difference between two squares.
9a((n2 + q2)(-1n2 + q2)) = 0

Factor a difference between two squares.
9a((n2 + q2)((n + q)(-1n + q))) = 0

Ignore the factor 9.

Subproblem 1

Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0

Subproblem 2

Set the factor '(n2 + q2)' equal to zero and attempt to solve: Simplifying n2 + q2 = 0 Solving n2 + q2 = 0 Move all terms containing a to the left, all other terms to the right. Add '-1n2' to each side of the equation. n2 + -1n2 + q2 = 0 + -1n2 Combine like terms: n2 + -1n2 = 0 0 + q2 = 0 + -1n2 q2 = 0 + -1n2 Remove the zero: q2 = -1n2 Add '-1q2' to each side of the equation. q2 + -1q2 = -1n2 + -1q2 Combine like terms: q2 + -1q2 = 0 0 = -1n2 + -1q2 Simplifying 0 = -1n2 + -1q2 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 '(n + q)' equal to zero and attempt to solve: Simplifying n + q = 0 Solving n + q = 0 Move all terms containing a to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n + q = 0 + -1n Combine like terms: n + -1n = 0 0 + q = 0 + -1n q = 0 + -1n Remove the zero: q = -1n Add '-1q' to each side of the equation. q + -1q = -1n + -1q Combine like terms: q + -1q = 0 0 = -1n + -1q Simplifying 0 = -1n + -1q 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 '(-1n + q)' equal to zero and attempt to solve: Simplifying -1n + q = 0 Solving -1n + q = 0 Move all terms containing a to the left, all other terms to the right. Add 'n' to each side of the equation. -1n + n + q = 0 + n Combine like terms: -1n + n = 0 0 + q = 0 + n q = 0 + n Remove the zero: q = n Add '-1q' to each side of the equation. q + -1q = n + -1q Combine like terms: q + -1q = 0 0 = n + -1q Simplifying 0 = n + -1q The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

a = {0}

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