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

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

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

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

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

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

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

Reorder the terms:
6 + 11y + 4y2 = -3(3 + 4y)
6 + 11y + 4y2 = (3 * -3 + 4y * -3)
6 + 11y + 4y2 = (-9 + -12y)

Solving
6 + 11y + 4y2 = -9 + -12y

Solving for variable 'y'.

Reorder the terms:
6 + 9 + 11y + 12y + 4y2 = -9 + -12y + 9 + 12y

Combine like terms: 6 + 9 = 15
15 + 11y + 12y + 4y2 = -9 + -12y + 9 + 12y

Combine like terms: 11y + 12y = 23y
15 + 23y + 4y2 = -9 + -12y + 9 + 12y

Reorder the terms:
15 + 23y + 4y2 = -9 + 9 + -12y + 12y

Combine like terms: -9 + 9 = 0
15 + 23y + 4y2 = 0 + -12y + 12y
15 + 23y + 4y2 = -12y + 12y

Combine like terms: -12y + 12y = 0
15 + 23y + 4y2 = 0

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

Subproblem 1
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

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

Add '-5' to each side of the equation.
5 + -5 + y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + y = 0 + -5
y = 0 + -5

Combine like terms: 0 + -5 = -5
y = -5

Simplifying
y = -5
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 = {-5, -0.75}