10w^4=2w^2

Solution for 10w^4=2w^2 equation:

Simplifying
10w4 = 2w2

Solving
10w4 = 2w2

Solving for variable 'w'.

Reorder the terms:
-2w2 + 10w4 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
-2w2 + 10w4 = 0

Factor out the Greatest Common Factor (GCF), '2w2'.
2w2(-1 + 5w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'w2' equal to zero and attempt to solve:

Simplifying
w2 = 0

Solving
w2 = 0

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

Simplifying
w2 = 0

Take the square root of each side:
w = {0}
Subproblem 2
Set the factor '(-1 + 5w2)' equal to zero and attempt to solve:

Simplifying
-1 + 5w2 = 0

Solving
-1 + 5w2 = 0

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

Add '1' to each side of the equation.
-1 + 1 + 5w2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 5w2 = 0 + 1
5w2 = 0 + 1

Combine like terms: 0 + 1 = 1
5w2 = 1

Divide each side by '5'.
w2 = 0.2

Simplifying
w2 = 0.2

Take the square root of each side:
w = {-0.447213596, 0.447213596}
Solution
w = {0, -0.447213596, 0.447213596}