(3y+7)(5+y)=0

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Solution for (3y+7)(5+y)=0 equation: 


Simplifying
(3y + 7)(5 + y) = 0

Reorder the terms:
(7 + 3y)(5 + y) = 0

Multiply (7 + 3y) * (5 + y)
(7(5 + y) + 3y * (5 + y)) = 0
((5 * 7 + y * 7) + 3y * (5 + y)) = 0
((35 + 7y) + 3y * (5 + y)) = 0
(35 + 7y + (5 * 3y + y * 3y)) = 0
(35 + 7y + (15y + 3y2)) = 0

Combine like terms: 7y + 15y = 22y
(35 + 22y + 3y2) = 0

Solving
35 + 22y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5 + y)(7 + 3y) = 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 '(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 = {-5, -2.333333333}

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