2w^4(2w^2+13w+6)=0

Solution for 2w^4(2w^2+13w+6)=0 equation:

Simplifying
2w4(2w2 + 13w + 6) = 0

Reorder the terms:
2w4(6 + 13w + 2w2) = 0
(6 * 2w4 + 13w * 2w4 + 2w2 * 2w4) = 0
(12w4 + 26w5 + 4w6) = 0

Solving
12w4 + 26w5 + 4w6 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2w4'.
2w4(6 + 13w + 2w2) = 0

Factor a trinomial.
2w4((6 + w)(1 + 2w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'w4' equal to zero and attempt to solve:

Simplifying
w4 = 0

Solving
w4 = 0

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

Simplifying
w4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

Solving
6 + w = 0

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

Add '-6' to each side of the equation.
6 + -6 + w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + w = 0 + -6
w = 0 + -6

Combine like terms: 0 + -6 = -6
w = -6

Simplifying
w = -6
Subproblem 3
Set the factor '(1 + 2w)' equal to zero and attempt to solve:

Simplifying
1 + 2w = 0

Solving
1 + 2w = 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 + 2w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2w = 0 + -1
2w = 0 + -1

Combine like terms: 0 + -1 = -1
2w = -1

Divide each side by '2'.
w = -0.5

Simplifying
w = -0.5
Solution
w = {-6, -0.5}