5w^8-45w^7-50w^6=0

Solution for 5w^8-45w^7-50w^6=0 equation:

Simplifying
5w8 + -45w7 + -50w6 = 0

Reorder the terms:
-50w6 + -45w7 + 5w8 = 0

Solving
-50w6 + -45w7 + 5w8 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5w6'.
5w6(-10 + -9w + w2) = 0

Factor a trinomial.
5w6((-1 + -1w)(10 + -1w)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'w6' equal to zero and attempt to solve:

Simplifying
w6 = 0

Solving
w6 = 0

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

Simplifying
w6 = 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 + -1w)' equal to zero and attempt to solve:

Simplifying
-1 + -1w = 0

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

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

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

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

Simplifying
w = -1
Subproblem 3
Set the factor '(10 + -1w)' equal to zero and attempt to solve:

Simplifying
10 + -1w = 0

Solving
10 + -1w = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1w = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1w = 0 + -10
-1w = 0 + -10

Combine like terms: 0 + -10 = -10
-1w = -10

Divide each side by '-1'.
w = 10

Simplifying
w = 10
Solution
w = {-1, 10}