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

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

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

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

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

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

Combine like terms: -8y + -1y = -9y
3(4 + -9y + 2y2) = 0
(4 * 3 + -9y * 3 + 2y2 * 3) = 0
(12 + -27y + 6y2) = 0

Solving
12 + -27y + 6y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -9y + 2y2) = 0

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

Ignore the factor 3.
Subproblem 1
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 2
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}