5y^2(5y+4)(y-6)=

Solution for 5y^2(5y+4)(y-6)= equation:

Simplifying
5y2(5y + 4)(y + -6) = 0

Reorder the terms:
5y2(4 + 5y)(y + -6) = 0

Reorder the terms:
5y2(4 + 5y)(-6 + y) = 0

Multiply (4 + 5y) * (-6 + y)
5y2(4(-6 + y) + 5y * (-6 + y)) = 0
5y2((-6 * 4 + y * 4) + 5y * (-6 + y)) = 0
5y2((-24 + 4y) + 5y * (-6 + y)) = 0
5y2(-24 + 4y + (-6 * 5y + y * 5y)) = 0
5y2(-24 + 4y + (-30y + 5y2)) = 0

Combine like terms: 4y + -30y = -26y
5y2(-24 + -26y + 5y2) = 0
(-24 * 5y2 + -26y * 5y2 + 5y2 * 5y2) = 0
(-120y2 + -130y3 + 25y4) = 0

Solving
-120y2 + -130y3 + 25y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5y2'.
5y2(-24 + -26y + 5y2) = 0

Factor a trinomial.
5y2((-4 + -5y)(6 + -1y)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve:

Simplifying
y2 = 0

Solving
y2 = 0

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

Simplifying
y2 = 0

Take the square root of each side:
y = {0}
Subproblem 2
Set the factor '(-4 + -5y)' equal to zero and attempt to solve:

Simplifying
-4 + -5y = 0

Solving
-4 + -5y = 0

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

Add '4' to each side of the equation.
-4 + 4 + -5y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5y = 0 + 4
-5y = 0 + 4

Combine like terms: 0 + 4 = 4
-5y = 4

Divide each side by '-5'.
y = -0.8

Simplifying
y = -0.8
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 = {0, -0.8, 6}