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

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

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

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

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

Combine like terms: 3y + 8y = 11y
(6 + 11y + 4y2) = 0

Solving
6 + 11y + 4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(2 + y)(3 + 4y) = 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 '(3 + 4y)' equal to zero and attempt to solve:

Simplifying
3 + 4y = 0

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

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

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

Divide each side by '4'.
y = -0.75

Simplifying
y = -0.75
Solution
y = {-2, -0.75}