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

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

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

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

Multiply (2 + y) * (4 + 3y)
(2(4 + 3y) + y(4 + 3y)) = 0
((4 * 2 + 3y * 2) + y(4 + 3y)) = 0
((8 + 6y) + y(4 + 3y)) = 0
(8 + 6y + (4 * y + 3y * y)) = 0
(8 + 6y + (4y + 3y2)) = 0

Combine like terms: 6y + 4y = 10y
(8 + 10y + 3y2) = 0

Solving
8 + 10y + 3y2 = 0

Solving for variable 'y'.

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

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

Simplifying
2 + y = 0

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

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

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

Simplifying
y = -2
Subproblem 2
Set the factor '(4 + 3y)' equal to zero and attempt to solve:

Simplifying
4 + 3y = 0

Solving
4 + 3y = 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 + 3y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3y = 0 + -4
3y = 0 + -4

Combine like terms: 0 + -4 = -4
3y = -4

Divide each side by '3'.
y = -1.333333333

Simplifying
y = -1.333333333
Solution
y = {-2, -1.333333333}