3y(2y+1)(y-4)=0

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Solution for 3y(2y+1)(y-4)=0 equation: 


Simplifying
3y(2y + 1)(y + -4) = 0

Reorder the terms:
3y(1 + 2y)(y + -4) = 0

Reorder the terms:
3y(1 + 2y)(-4 + y) = 0

Multiply (1 + 2y) * (-4 + y)
3y(1(-4 + y) + 2y * (-4 + y)) = 0
3y((-4 * 1 + y * 1) + 2y * (-4 + y)) = 0
3y((-4 + 1y) + 2y * (-4 + y)) = 0
3y(-4 + 1y + (-4 * 2y + y * 2y)) = 0
3y(-4 + 1y + (-8y + 2y2)) = 0

Combine like terms: 1y + -8y = -7y
3y(-4 + -7y + 2y2) = 0
(-4 * 3y + -7y * 3y + 2y2 * 3y) = 0
(-12y + -21y2 + 6y3) = 0

Solving
-12y + -21y2 + 6y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(-4 + -7y + 2y2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

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, -0.5, 4}

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