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

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

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

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

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

Multiply (1 + 4y) * (2 + 3y)
3(1(2 + 3y) + 4y * (2 + 3y)) = 0
3((2 * 1 + 3y * 1) + 4y * (2 + 3y)) = 0
3((2 + 3y) + 4y * (2 + 3y)) = 0
3(2 + 3y + (2 * 4y + 3y * 4y)) = 0
3(2 + 3y + (8y + 12y2)) = 0

Combine like terms: 3y + 8y = 11y
3(2 + 11y + 12y2) = 0
(2 * 3 + 11y * 3 + 12y2 * 3) = 0
(6 + 33y + 36y2) = 0

Solving
6 + 33y + 36y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 11y + 12y2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + 3y)' equal to zero and attempt to solve:

Simplifying
2 + 3y = 0

Solving
2 + 3y = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3y = 0 + -2
3y = 0 + -2

Combine like terms: 0 + -2 = -2
3y = -2

Divide each side by '3'.
y = -0.6666666667

Simplifying
y = -0.6666666667
Subproblem 2
Set the factor '(1 + 4y)' equal to zero and attempt to solve:

Simplifying
1 + 4y = 0

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

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

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

Divide each side by '4'.
y = -0.25

Simplifying
y = -0.25
Solution
y = {-0.6666666667, -0.25}