10y^7+32y^6+6y^5=0

Solution for 10y^7+32y^6+6y^5=0 equation:

Simplifying
10y7 + 32y6 + 6y5 = 0

Reorder the terms:
6y5 + 32y6 + 10y7 = 0

Solving
6y5 + 32y6 + 10y7 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y5'.
2y5(3 + 16y + 5y2) = 0

Factor a trinomial.
2y5((3 + y)(1 + 5y)) = 0

Ignore the factor 2.
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 '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

Add '-3' to each side of the equation.
3 + -3 + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

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

Simplifying
1 + 5y = 0

Solving
1 + 5y = 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 + 5y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5y = 0 + -1
5y = 0 + -1

Combine like terms: 0 + -1 = -1
5y = -1

Divide each side by '5'.
y = -0.2

Simplifying
y = -0.2
Solution
y = {-3, -0.2}