(w^2+1)-(3w^2-2)=0

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

Simplifying
(w2 + 1) + -1(3w2 + -2) = 0

Reorder the terms:
(1 + w2) + -1(3w2 + -2) = 0

Remove parenthesis around (1 + w2)
1 + w2 + -1(3w2 + -2) = 0

Reorder the terms:
1 + w2 + -1(-2 + 3w2) = 0
1 + w2 + (-2 * -1 + 3w2 * -1) = 0
1 + w2 + (2 + -3w2) = 0

Reorder the terms:
1 + 2 + w2 + -3w2 = 0

Combine like terms: 1 + 2 = 3
3 + w2 + -3w2 = 0

Combine like terms: w2 + -3w2 = -2w2
3 + -2w2 = 0

Solving
3 + -2w2 = 0

Solving for variable 'w'.

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

Add '-3' to each side of the equation.
3 + -3 + -2w2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2w2 = 0 + -3
-2w2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2w2 = -3

Divide each side by '-2'.
w2 = 1.5

Simplifying
w2 = 1.5

Take the square root of each side:
w = {-1.224744871, 1.224744871}