(3y+2)(y+3)=-5(3y+2)

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Solution for (3y+2)(y+3)=-5(3y+2) equation: 


Simplifying
(3y + 2)(y + 3) = -5(3y + 2)

Reorder the terms:
(2 + 3y)(y + 3) = -5(3y + 2)

Reorder the terms:
(2 + 3y)(3 + y) = -5(3y + 2)

Multiply (2 + 3y) * (3 + y)
(2(3 + y) + 3y * (3 + y)) = -5(3y + 2)
((3 * 2 + y * 2) + 3y * (3 + y)) = -5(3y + 2)
((6 + 2y) + 3y * (3 + y)) = -5(3y + 2)
(6 + 2y + (3 * 3y + y * 3y)) = -5(3y + 2)
(6 + 2y + (9y + 3y2)) = -5(3y + 2)

Combine like terms: 2y + 9y = 11y
(6 + 11y + 3y2) = -5(3y + 2)

Reorder the terms:
6 + 11y + 3y2 = -5(2 + 3y)
6 + 11y + 3y2 = (2 * -5 + 3y * -5)
6 + 11y + 3y2 = (-10 + -15y)

Solving
6 + 11y + 3y2 = -10 + -15y

Solving for variable 'y'.

Reorder the terms:
6 + 10 + 11y + 15y + 3y2 = -10 + -15y + 10 + 15y

Combine like terms: 6 + 10 = 16
16 + 11y + 15y + 3y2 = -10 + -15y + 10 + 15y

Combine like terms: 11y + 15y = 26y
16 + 26y + 3y2 = -10 + -15y + 10 + 15y

Reorder the terms:
16 + 26y + 3y2 = -10 + 10 + -15y + 15y

Combine like terms: -10 + 10 = 0
16 + 26y + 3y2 = 0 + -15y + 15y
16 + 26y + 3y2 = -15y + 15y

Combine like terms: -15y + 15y = 0
16 + 26y + 3y2 = 0

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


Subproblem 1
Set the factor '(8 + y)' equal to zero and attempt to solve:

Simplifying
8 + y = 0

Solving
8 + y = 0

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

Add '-8' to each side of the equation.
8 + -8 + y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + y = 0 + -8
y = 0 + -8

Combine like terms: 0 + -8 = -8
y = -8

Simplifying
y = -8

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 = {-8, -0.6666666667}

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