5y^4((5+2y)(1+y))=0

Solution for 5y^4((5+2y)(1+y))=0 equation:

Simplifying
5y4((5 + 2y)(1 + y)) = 0

Multiply (5 + 2y) * (1 + y)
5y4((5(1 + y) + 2y * (1 + y))) = 0
5y4(((1 * 5 + y * 5) + 2y * (1 + y))) = 0
5y4(((5 + 5y) + 2y * (1 + y))) = 0
5y4((5 + 5y + (1 * 2y + y * 2y))) = 0
5y4((5 + 5y + (2y + 2y2))) = 0

Combine like terms: 5y + 2y = 7y
5y4((5 + 7y + 2y2)) = 0
(5 * 5y4 + 7y * 5y4 + 2y2 * 5y4) = 0
(25y4 + 35y5 + 10y6) = 0

Solving
25y4 + 35y5 + 10y6 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y4'.
5y4(5 + 7y + 2y2) = 0

Factor a trinomial.
5y4((5 + 2y)(1 + y)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'y4' equal to zero and attempt to solve:

Simplifying
y4 = 0

Solving
y4 = 0

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

Simplifying
y4 = 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 '(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
Subproblem 3
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

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

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

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

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