x^9+5x^8w-24x^7w^2=0

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Solution for x^9+5x^8w-24x^7w^2=0 equation: 


Simplifying
x9 + 5x8w + -24x7w2 = 0

Reorder the terms:
5wx8 + -24w2x7 + x9 = 0

Solving
5wx8 + -24w2x7 + x9 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), 'x7'.
x7(5wx + -24w2 + x2) = 0

Factor a trinomial.
x7((-8w + -1x)(3w + -1x)) = 0


Subproblem 1
Set the factor 'x7' equal to zero and attempt to solve:

Simplifying
x7 = 0

Solving
x7 = 0

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

Add '-1x7' to each side of the equation.
x7 + -1x7 = 0 + -1x7
Remove the zero:
0 = -1x7

Simplifying
0 = -1x7

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 '(-8w + -1x)' equal to zero and attempt to solve:

Simplifying
-8w + -1x = 0

Solving
-8w + -1x = 0

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

Add 'x' to each side of the equation.
-8w + -1x + x = 0 + x

Combine like terms: -1x + x = 0
-8w + 0 = 0 + x
-8w = 0 + x
Remove the zero:
-8w = x

Divide each side by '-8'.
w = -0.125x

Simplifying
w = -0.125x

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

Simplifying
3w + -1x = 0

Solving
3w + -1x = 0

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

Add 'x' to each side of the equation.
3w + -1x + x = 0 + x

Combine like terms: -1x + x = 0
3w + 0 = 0 + x
3w = 0 + x
Remove the zero:
3w = x

Divide each side by '3'.
w = 0.3333333333x

Simplifying
w = 0.3333333333x
Solution
w = {-0.125x, 0.3333333333x}

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