0=6w^7-27w^6+27w^5

Solution for 0=6w^7-27w^6+27w^5 equation:

Simplifying
0 = 6w7 + -27w6 + 27w5

Reorder the terms:
0 = 27w5 + -27w6 + 6w7

Solving
0 = 27w5 + -27w6 + 6w7

Solving for variable 'w'.
Remove the zero:
-27w5 + 27w6 + -6w7 = 27w5 + -27w6 + 6w7 + -27w5 + 27w6 + -6w7

Reorder the terms:
-27w5 + 27w6 + -6w7 = 27w5 + -27w5 + -27w6 + 27w6 + 6w7 + -6w7

Combine like terms: 27w5 + -27w5 = 0
-27w5 + 27w6 + -6w7 = 0 + -27w6 + 27w6 + 6w7 + -6w7
-27w5 + 27w6 + -6w7 = -27w6 + 27w6 + 6w7 + -6w7

Combine like terms: -27w6 + 27w6 = 0
-27w5 + 27w6 + -6w7 = 0 + 6w7 + -6w7
-27w5 + 27w6 + -6w7 = 6w7 + -6w7

Combine like terms: 6w7 + -6w7 = 0
-27w5 + 27w6 + -6w7 = 0

Factor out the Greatest Common Factor (GCF), '3w5'.
3w5(-9 + 9w + -2w2) = 0

Factor a trinomial.
3w5((-3 + w)(3 + -2w)) = 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 '(-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 '(3 + -2w)' equal to zero and attempt to solve:

Simplifying
3 + -2w = 0

Solving
3 + -2w = 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 + -2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2w = 0 + -3
-2w = 0 + -3

Combine like terms: 0 + -3 = -3
-2w = -3

Divide each side by '-2'.
w = 1.5

Simplifying
w = 1.5
Solution
w = {3, 1.5}