(3y+5)(8+y)=0

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Solution for (3y+5)(8+y)=0 equation: 


Simplifying
(3y + 5)(8 + y) = 0

Reorder the terms:
(5 + 3y)(8 + y) = 0

Multiply (5 + 3y) * (8 + y)
(5(8 + y) + 3y * (8 + y)) = 0
((8 * 5 + y * 5) + 3y * (8 + y)) = 0
((40 + 5y) + 3y * (8 + y)) = 0
(40 + 5y + (8 * 3y + y * 3y)) = 0
(40 + 5y + (24y + 3y2)) = 0

Combine like terms: 5y + 24y = 29y
(40 + 29y + 3y2) = 0

Solving
40 + 29y + 3y2 = 0

Solving for variable 'y'.

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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