10y^7-15y^6-25y^5=0

Solution for 10y^7-15y^6-25y^5=0 equation:

Simplifying
10y7 + -15y6 + -25y5 = 0

Reorder the terms:
-25y5 + -15y6 + 10y7 = 0

Solving
-25y5 + -15y6 + 10y7 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y5'.
5y5(-5 + -3y + 2y2) = 0

Factor a trinomial.
5y5((-1 + -1y)(5 + -2y)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'y5' equal to zero and attempt to solve:

Simplifying
y5 = 0

Solving
y5 = 0

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

Simplifying
y5 = 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 + -1y)' equal to zero and attempt to solve:

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 0

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

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

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

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

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

Simplifying
y = -1
Subproblem 3
Set the factor '(5 + -2y)' equal to zero and attempt to solve:

Simplifying
5 + -2y = 0

Solving
5 + -2y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2y = 0 + -5
-2y = 0 + -5

Combine like terms: 0 + -5 = -5
-2y = -5

Divide each side by '-2'.
y = 2.5

Simplifying
y = 2.5
Solution
y = {-1, 2.5}