2y^3(2y+1)(y-4)=

Solution for 2y^3(2y+1)(y-4)= equation:

Simplifying
2y3(2y + 1)(y + -4) = 0

Reorder the terms:
2y3(1 + 2y)(y + -4) = 0

Reorder the terms:
2y3(1 + 2y)(-4 + y) = 0

Multiply (1 + 2y) * (-4 + y)
2y3(1(-4 + y) + 2y * (-4 + y)) = 0
2y3((-4 * 1 + y * 1) + 2y * (-4 + y)) = 0
2y3((-4 + 1y) + 2y * (-4 + y)) = 0
2y3(-4 + 1y + (-4 * 2y + y * 2y)) = 0
2y3(-4 + 1y + (-8y + 2y2)) = 0

Combine like terms: 1y + -8y = -7y
2y3(-4 + -7y + 2y2) = 0
(-4 * 2y3 + -7y * 2y3 + 2y2 * 2y3) = 0
(-8y3 + -14y4 + 4y5) = 0

Solving
-8y3 + -14y4 + 4y5 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y3'.
2y3(-4 + -7y + 2y2) = 0

Factor a trinomial.
2y3((-1 + -2y)(4 + -1y)) = 0

Ignore the factor 2.
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 '(-1 + -2y)' equal to zero and attempt to solve:

Simplifying
-1 + -2y = 0

Solving
-1 + -2y = 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 + -2y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2y = 0 + 1
-2y = 0 + 1

Combine like terms: 0 + 1 = 1
-2y = 1

Divide each side by '-2'.
y = -0.5

Simplifying
y = -0.5
Subproblem 3
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 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 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {-0.5, 4}