10w^6+34w^5+12w^4=0

Solution for 10w^6+34w^5+12w^4=0 equation:

Simplifying
10w6 + 34w5 + 12w4 = 0

Reorder the terms:
12w4 + 34w5 + 10w6 = 0

Solving
12w4 + 34w5 + 10w6 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2w4'.
2w4(6 + 17w + 5w2) = 0

Factor a trinomial.
2w4((3 + w)(2 + 5w)) = 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 '(3 + w)' equal to zero and attempt to solve:

Simplifying
3 + w = 0

Solving
3 + w = 0

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

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

Combine like terms: 3 + -3 = 0
0 + w = 0 + -3
w = 0 + -3

Combine like terms: 0 + -3 = -3
w = -3

Simplifying
w = -3
Subproblem 3
Set the factor '(2 + 5w)' equal to zero and attempt to solve:

Simplifying
2 + 5w = 0

Solving
2 + 5w = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5w = 0 + -2
5w = 0 + -2

Combine like terms: 0 + -2 = -2
5w = -2

Divide each side by '5'.
w = -0.4

Simplifying
w = -0.4
Solution
w = {-3, -0.4}