(v^2+gn)(v^2-gn)=

Solution for (v^2+gn)(v^2-gn)= equation:

Simplifying
(v2 + gn)(v2 + -1gn) = 0

Reorder the terms:
(gn + v2)(v2 + -1gn) = 0

Reorder the terms:
(gn + v2)(-1gn + v2) = 0

Multiply (gn + v2) * (-1gn + v2)
(gn(-1gn + v2) + v2(-1gn + v2)) = 0
((-1gn * gn + v2 * gn) + v2(-1gn + v2)) = 0

Reorder the terms:
((gnv2 + -1g2n2) + v2(-1gn + v2)) = 0
((gnv2 + -1g2n2) + v2(-1gn + v2)) = 0
(gnv2 + -1g2n2 + (-1gn * v2 + v2 * v2)) = 0
(gnv2 + -1g2n2 + (-1gnv2 + v4)) = 0

Reorder the terms:
(gnv2 + -1gnv2 + -1g2n2 + v4) = 0

Combine like terms: gnv2 + -1gnv2 = 0
(0 + -1g2n2 + v4) = 0
(-1g2n2 + v4) = 0

Solving
-1g2n2 + v4 = 0

Solving for variable 'g'.

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

Add '-1v4' to each side of the equation.
-1g2n2 + v4 + -1v4 = 0 + -1v4

Combine like terms: v4 + -1v4 = 0
-1g2n2 + 0 = 0 + -1v4
-1g2n2 = 0 + -1v4
Remove the zero:
-1g2n2 = -1v4

Divide each side by '-1n2'.
g2 = n-2v4

Simplifying
g2 = n-2v4

Take the square root of each side:
g = {-1n-1v2, n-1v2}