6w^7-39w^6+18w^5=0

Solution for 6w^7-39w^6+18w^5=0 equation:

Simplifying
6w7 + -39w6 + 18w5 = 0

Reorder the terms:
18w5 + -39w6 + 6w7 = 0

Solving
18w5 + -39w6 + 6w7 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3w5'.
3w5(6 + -13w + 2w2) = 0

Factor a trinomial.
3w5((1 + -2w)(6 + -1w)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'w5' equal to zero and attempt to solve:

Simplifying
w5 = 0

Solving
w5 = 0

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

Simplifying
w5 = 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 + -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
Subproblem 3
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 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 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

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