y(5y^2-39y-8)=0

Solution for y(5y^2-39y-8)=0 equation:

Simplifying
y(5y2 + -39y + -8) = 0

Reorder the terms:
y(-8 + -39y + 5y2) = 0
(-8 * y + -39y * y + 5y2 * y) = 0
(-8y + -39y2 + 5y3) = 0

Solving
-8y + -39y2 + 5y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(-8 + -39y + 5y2) = 0

Factor a trinomial.
y((-1 + -5y)(8 + -1y)) = 0

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

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
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
Subproblem 3
Set the factor '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 0

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

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

Combine like terms: 8 + -8 = 0
0 + -1y = 0 + -8
-1y = 0 + -8

Combine like terms: 0 + -8 = -8
-1y = -8

Divide each side by '-1'.
y = 8

Simplifying
y = 8
Solution
y = {0, -0.2, 8}