3*w^2+w^2-1=0

Solution for 3*w^2+w^2-1=0 equation:

Simplifying
3w2 + w2 + -1 = 0

Reorder the terms:
-1 + 3w2 + w2 = 0

Combine like terms: 3w2 + w2 = 4w2
-1 + 4w2 = 0

Solving
-1 + 4w2 = 0

Solving for variable 'w'.

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

Add '1' to each side of the equation.
-1 + 1 + 4w2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4w2 = 0 + 1
4w2 = 0 + 1

Combine like terms: 0 + 1 = 1
4w2 = 1

Divide each side by '4'.
w2 = 0.25

Simplifying
w2 = 0.25

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