2y^2(3y+5)(y-4)=

Solution for 2y^2(3y+5)(y-4)= equation:

Simplifying
2y2(3y + 5)(y + -4) = 0

Reorder the terms:
2y2(5 + 3y)(y + -4) = 0

Reorder the terms:
2y2(5 + 3y)(-4 + y) = 0

Multiply (5 + 3y) * (-4 + y)
2y2(5(-4 + y) + 3y * (-4 + y)) = 0
2y2((-4 * 5 + y * 5) + 3y * (-4 + y)) = 0
2y2((-20 + 5y) + 3y * (-4 + y)) = 0
2y2(-20 + 5y + (-4 * 3y + y * 3y)) = 0
2y2(-20 + 5y + (-12y + 3y2)) = 0

Combine like terms: 5y + -12y = -7y
2y2(-20 + -7y + 3y2) = 0
(-20 * 2y2 + -7y * 2y2 + 3y2 * 2y2) = 0
(-40y2 + -14y3 + 6y4) = 0

Solving
-40y2 + -14y3 + 6y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y2'.
2y2(-20 + -7y + 3y2) = 0

Factor a trinomial.
2y2((-5 + -3y)(4 + -1y)) = 0

Ignore the factor 2.
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 '(-5 + -3y)' equal to zero and attempt to solve:

Simplifying
-5 + -3y = 0

Solving
-5 + -3y = 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 + -3y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3y = 0 + 5
-3y = 0 + 5

Combine like terms: 0 + 5 = 5
-3y = 5

Divide each side by '-3'.
y = -1.666666667

Simplifying
y = -1.666666667
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, -1.666666667, 4}