(3y+7)(8+y)=0

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Solution for (3y+7)(8+y)=0 equation: 


Simplifying
(3y + 7)(8 + y) = 0

Reorder the terms:
(7 + 3y)(8 + y) = 0

Multiply (7 + 3y) * (8 + y)
(7(8 + y) + 3y * (8 + y)) = 0
((8 * 7 + y * 7) + 3y * (8 + y)) = 0
((56 + 7y) + 3y * (8 + y)) = 0
(56 + 7y + (8 * 3y + y * 3y)) = 0
(56 + 7y + (24y + 3y2)) = 0

Combine like terms: 7y + 24y = 31y
(56 + 31y + 3y2) = 0

Solving
56 + 31y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(8 + y)(7 + 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 '(7 + 3y)' equal to zero and attempt to solve:

Simplifying
7 + 3y = 0

Solving
7 + 3y = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3y = 0 + -7
3y = 0 + -7

Combine like terms: 0 + -7 = -7
3y = -7

Divide each side by '3'.
y = -2.333333333

Simplifying
y = -2.333333333
Solution
y = {-8, -2.333333333}

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