(5+y)(3y+2)=0

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Solution for (5+y)(3y+2)=0 equation: 


Simplifying
(5 + y)(3y + 2) = 0

Reorder the terms:
(5 + y)(2 + 3y) = 0

Multiply (5 + y) * (2 + 3y)
(5(2 + 3y) + y(2 + 3y)) = 0
((2 * 5 + 3y * 5) + y(2 + 3y)) = 0
((10 + 15y) + y(2 + 3y)) = 0
(10 + 15y + (2 * y + 3y * y)) = 0
(10 + 15y + (2y + 3y2)) = 0

Combine like terms: 15y + 2y = 17y
(10 + 17y + 3y2) = 0

Solving
10 + 17y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5 + y)(2 + 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 '(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 = {-5, -0.6666666667}

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