4sq^4-4sn^4=0

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Solution for 4sq^4-4sn^4=0 equation:


Simplifying
4sq4 + -4sn4 = 0

Reorder the terms:
-4n4s + 4q4s = 0

Solving
-4n4s + 4q4s = 0

Solving for variable 'n'.

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

Add '-4q4s' to each side of the equation.
-4n4s + 4q4s + -4q4s = 0 + -4q4s

Combine like terms: 4q4s + -4q4s = 0
-4n4s + 0 = 0 + -4q4s
-4n4s = 0 + -4q4s
Remove the zero:
-4n4s = -4q4s

Divide each side by '-4s'.
n4 = q4

Simplifying
n4 = q4

Combine like terms: q4 + -1q4 = 0
n4 + -1q4 = 0

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

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

Subproblem 1

Set the factor '(n2 + q2)' equal to zero and attempt to solve: Simplifying n2 + q2 = 0 Solving n2 + q2 = 0 Move all terms containing n to the left, all other terms to the right. Add '-1q2' to each side of the equation. n2 + q2 + -1q2 = 0 + -1q2 Combine like terms: q2 + -1q2 = 0 n2 + 0 = 0 + -1q2 n2 = 0 + -1q2 Remove the zero: n2 = -1q2 Simplifying n2 = -1q2 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 '(n + q)' equal to zero and attempt to solve: Simplifying n + q = 0 Solving n + q = 0 Move all terms containing n to the left, all other terms to the right. Add '-1q' to each side of the equation. n + q + -1q = 0 + -1q Combine like terms: q + -1q = 0 n + 0 = 0 + -1q n = 0 + -1q Remove the zero: n = -1q Simplifying n = -1q

Subproblem 3

Set the factor '(n + -1q)' equal to zero and attempt to solve: Simplifying n + -1q = 0 Solving n + -1q = 0 Move all terms containing n to the left, all other terms to the right. Add 'q' to each side of the equation. n + -1q + q = 0 + q Combine like terms: -1q + q = 0 n + 0 = 0 + q n = 0 + q Remove the zero: n = q Simplifying n = q

Solution

n = {-1q, q}

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