10w^6-45w^5+45w^4=0

Solution for 10w^6-45w^5+45w^4=0 equation:

Simplifying
10w6 + -45w5 + 45w4 = 0

Reorder the terms:
45w4 + -45w5 + 10w6 = 0

Solving
45w4 + -45w5 + 10w6 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5w4'.
5w4(9 + -9w + 2w2) = 0

Factor a trinomial.
5w4((3 + -2w)(3 + -1w)) = 0

Ignore the factor 5.
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 + -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
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 = {1.5, 3}