5y^3(2y+5)(y-6)=

Solution for 5y^3(2y+5)(y-6)= equation:

Simplifying
5y3(2y + 5)(y + -6) = 0

Reorder the terms:
5y3(5 + 2y)(y + -6) = 0

Reorder the terms:
5y3(5 + 2y)(-6 + y) = 0

Multiply (5 + 2y) * (-6 + y)
5y3(5(-6 + y) + 2y * (-6 + y)) = 0
5y3((-6 * 5 + y * 5) + 2y * (-6 + y)) = 0
5y3((-30 + 5y) + 2y * (-6 + y)) = 0
5y3(-30 + 5y + (-6 * 2y + y * 2y)) = 0
5y3(-30 + 5y + (-12y + 2y2)) = 0

Combine like terms: 5y + -12y = -7y
5y3(-30 + -7y + 2y2) = 0
(-30 * 5y3 + -7y * 5y3 + 2y2 * 5y3) = 0
(-150y3 + -35y4 + 10y5) = 0

Solving
-150y3 + -35y4 + 10y5 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y3'.
5y3(-30 + -7y + 2y2) = 0

Factor a trinomial.
5y3((-5 + -2y)(6 + -1y)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'y3' equal to zero and attempt to solve:

Simplifying
y3 = 0

Solving
y3 = 0

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

Simplifying
y3 = 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 '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {-2.5, 6}