2u^2-1+6u^2-1=0

Solution for 2u^2-1+6u^2-1=0 equation:

Simplifying
2u2 + -1 + 6u2 + -1 = 0

Reorder the terms:
-1 + -1 + 2u2 + 6u2 = 0

Combine like terms: -1 + -1 = -2
-2 + 2u2 + 6u2 = 0

Combine like terms: 2u2 + 6u2 = 8u2
-2 + 8u2 = 0

Solving
-2 + 8u2 = 0

Solving for variable 'u'.

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

Add '2' to each side of the equation.
-2 + 2 + 8u2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 8u2 = 0 + 2
8u2 = 0 + 2

Combine like terms: 0 + 2 = 2
8u2 = 2

Divide each side by '8'.
u2 = 0.25

Simplifying
u2 = 0.25

Take the square root of each side:
u = {-0.5, 0.5}