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

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

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

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

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

Multiply (3 + 4y) * (3 + y)
(3(3 + y) + 4y * (3 + y)) = -2(4y + 3)
((3 * 3 + y * 3) + 4y * (3 + y)) = -2(4y + 3)
((9 + 3y) + 4y * (3 + y)) = -2(4y + 3)
(9 + 3y + (3 * 4y + y * 4y)) = -2(4y + 3)
(9 + 3y + (12y + 4y2)) = -2(4y + 3)

Combine like terms: 3y + 12y = 15y
(9 + 15y + 4y2) = -2(4y + 3)

Reorder the terms:
9 + 15y + 4y2 = -2(3 + 4y)
9 + 15y + 4y2 = (3 * -2 + 4y * -2)
9 + 15y + 4y2 = (-6 + -8y)

Solving
9 + 15y + 4y2 = -6 + -8y

Solving for variable 'y'.

Reorder the terms:
9 + 6 + 15y + 8y + 4y2 = -6 + -8y + 6 + 8y

Combine like terms: 9 + 6 = 15
15 + 15y + 8y + 4y2 = -6 + -8y + 6 + 8y

Combine like terms: 15y + 8y = 23y
15 + 23y + 4y2 = -6 + -8y + 6 + 8y

Reorder the terms:
15 + 23y + 4y2 = -6 + 6 + -8y + 8y

Combine like terms: -6 + 6 = 0
15 + 23y + 4y2 = 0 + -8y + 8y
15 + 23y + 4y2 = -8y + 8y

Combine like terms: -8y + 8y = 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}