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

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

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

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

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

Multiply (3 + 4y) * (-4 + y)
3y2(3(-4 + y) + 4y * (-4 + y)) = 0
3y2((-4 * 3 + y * 3) + 4y * (-4 + y)) = 0
3y2((-12 + 3y) + 4y * (-4 + y)) = 0
3y2(-12 + 3y + (-4 * 4y + y * 4y)) = 0
3y2(-12 + 3y + (-16y + 4y2)) = 0

Combine like terms: 3y + -16y = -13y
3y2(-12 + -13y + 4y2) = 0
(-12 * 3y2 + -13y * 3y2 + 4y2 * 3y2) = 0
(-36y2 + -39y3 + 12y4) = 0

Solving
-36y2 + -39y3 + 12y4 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3y2'.
3y2(-12 + -13y + 4y2) = 0

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

Ignore the factor 3.
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 '(-3 + -4y)' equal to zero and attempt to solve:

Simplifying
-3 + -4y = 0

Solving
-3 + -4y = 0

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

Add '3' to each side of the equation.
-3 + 3 + -4y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4y = 0 + 3
-4y = 0 + 3

Combine like terms: 0 + 3 = 3
-4y = 3

Divide each side by '-4'.
y = -0.75

Simplifying
y = -0.75
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, -0.75, 4}