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

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

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

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

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

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

Combine like terms: 2y + 12y = 14y
(8 + 14y + 3y2) = 3(3y + 2)

Reorder the terms:
8 + 14y + 3y2 = 3(2 + 3y)
8 + 14y + 3y2 = (2 * 3 + 3y * 3)
8 + 14y + 3y2 = (6 + 9y)

Solving
8 + 14y + 3y2 = 6 + 9y

Solving for variable 'y'.

Reorder the terms:
8 + -6 + 14y + -9y + 3y2 = 6 + 9y + -6 + -9y

Combine like terms: 8 + -6 = 2
2 + 14y + -9y + 3y2 = 6 + 9y + -6 + -9y

Combine like terms: 14y + -9y = 5y
2 + 5y + 3y2 = 6 + 9y + -6 + -9y

Reorder the terms:
2 + 5y + 3y2 = 6 + -6 + 9y + -9y

Combine like terms: 6 + -6 = 0
2 + 5y + 3y2 = 0 + 9y + -9y
2 + 5y + 3y2 = 9y + -9y

Combine like terms: 9y + -9y = 0
2 + 5y + 3y2 = 0

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

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

Simplifying
1 + y = 0

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

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

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

Simplifying
y = -1
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, -0.6666666667}