10w^5-28w^4-6w^3=0

Solution for 10w^5-28w^4-6w^3=0 equation:

Simplifying
10w5 + -28w4 + -6w3 = 0

Reorder the terms:
-6w3 + -28w4 + 10w5 = 0

Solving
-6w3 + -28w4 + 10w5 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2w3'.
2w3(-3 + -14w + 5w2) = 0

Factor a trinomial.
2w3((-1 + -5w)(3 + -1w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'w3' equal to zero and attempt to solve:

Simplifying
w3 = 0

Solving
w3 = 0

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

Simplifying
w3 = 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 '(-1 + -5w)' equal to zero and attempt to solve:

Simplifying
-1 + -5w = 0

Solving
-1 + -5w = 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 + -5w = 0 + 1

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

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

Divide each side by '-5'.
w = -0.2

Simplifying
w = -0.2
Subproblem 3
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 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 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Solution
w = {-0.2, 3}