6(3y+2)4(2y+3)=

Solution for 6(3y+2)4(2y+3)= equation:

Simplifying
6(3y + 2) * 4(2y + 3) = 0

Reorder the terms:
6(2 + 3y) * 4(2y + 3) = 0

Reorder the terms:
6(2 + 3y) * 4(3 + 2y) = 0

Reorder the terms for easier multiplication:
6 * 4(2 + 3y)(3 + 2y) = 0

Multiply 6 * 4
24(2 + 3y)(3 + 2y) = 0

Multiply (2 + 3y) * (3 + 2y)
24(2(3 + 2y) + 3y * (3 + 2y)) = 0
24((3 * 2 + 2y * 2) + 3y * (3 + 2y)) = 0
24((6 + 4y) + 3y * (3 + 2y)) = 0
24(6 + 4y + (3 * 3y + 2y * 3y)) = 0
24(6 + 4y + (9y + 6y2)) = 0

Combine like terms: 4y + 9y = 13y
24(6 + 13y + 6y2) = 0
(6 * 24 + 13y * 24 + 6y2 * 24) = 0
(144 + 312y + 144y2) = 0

Solving
144 + 312y + 144y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '24'.
24(6 + 13y + 6y2) = 0

Factor a trinomial.
24((3 + 2y)(2 + 3y)) = 0

Ignore the factor 24.
Subproblem 1
Set the factor '(3 + 2y)' equal to zero and attempt to solve:

Simplifying
3 + 2y = 0

Solving
3 + 2y = 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 + 2y = 0 + -3

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

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

Divide each side by '2'.
y = -1.5

Simplifying
y = -1.5
Subproblem 2
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
Solution
y = {-1.5, -0.6666666667}