(3y+5)(y+6)=-2(3y+5)

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Solution for (3y+5)(y+6)=-2(3y+5) equation: 


Simplifying
(3y + 5)(y + 6) = -2(3y + 5)

Reorder the terms:
(5 + 3y)(y + 6) = -2(3y + 5)

Reorder the terms:
(5 + 3y)(6 + y) = -2(3y + 5)

Multiply (5 + 3y) * (6 + y)
(5(6 + y) + 3y * (6 + y)) = -2(3y + 5)
((6 * 5 + y * 5) + 3y * (6 + y)) = -2(3y + 5)
((30 + 5y) + 3y * (6 + y)) = -2(3y + 5)
(30 + 5y + (6 * 3y + y * 3y)) = -2(3y + 5)
(30 + 5y + (18y + 3y2)) = -2(3y + 5)

Combine like terms: 5y + 18y = 23y
(30 + 23y + 3y2) = -2(3y + 5)

Reorder the terms:
30 + 23y + 3y2 = -2(5 + 3y)
30 + 23y + 3y2 = (5 * -2 + 3y * -2)
30 + 23y + 3y2 = (-10 + -6y)

Solving
30 + 23y + 3y2 = -10 + -6y

Solving for variable 'y'.

Reorder the terms:
30 + 10 + 23y + 6y + 3y2 = -10 + -6y + 10 + 6y

Combine like terms: 30 + 10 = 40
40 + 23y + 6y + 3y2 = -10 + -6y + 10 + 6y

Combine like terms: 23y + 6y = 29y
40 + 29y + 3y2 = -10 + -6y + 10 + 6y

Reorder the terms:
40 + 29y + 3y2 = -10 + 10 + -6y + 6y

Combine like terms: -10 + 10 = 0
40 + 29y + 3y2 = 0 + -6y + 6y
40 + 29y + 3y2 = -6y + 6y

Combine like terms: -6y + 6y = 0
40 + 29y + 3y2 = 0

Factor a trinomial.
(8 + y)(5 + 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 '(5 + 3y)' equal to zero and attempt to solve:

Simplifying
5 + 3y = 0

Solving
5 + 3y = 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 + 3y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3y = 0 + -5
3y = 0 + -5

Combine like terms: 0 + -5 = -5
3y = -5

Divide each side by '3'.
y = -1.666666667

Simplifying
y = -1.666666667
Solution
y = {-8, -1.666666667}

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