(4y+2)(5+y)=0

Solution for (4y+2)(5+y)=0 equation:

Simplifying
(4y + 2)(5 + y) = 0

Reorder the terms:
(2 + 4y)(5 + y) = 0

Multiply (2 + 4y) * (5 + y)
(2(5 + y) + 4y * (5 + y)) = 0
((5 * 2 + y * 2) + 4y * (5 + y)) = 0
((10 + 2y) + 4y * (5 + y)) = 0
(10 + 2y + (5 * 4y + y * 4y)) = 0
(10 + 2y + (20y + 4y2)) = 0

Combine like terms: 2y + 20y = 22y
(10 + 22y + 4y2) = 0

Solving
10 + 22y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 11y + 2y2) = 0

Factor a trinomial.
2((5 + y)(1 + 2y)) = 0

Ignore the factor 2.
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 '(1 + 2y)' equal to zero and attempt to solve:

Simplifying
1 + 2y = 0

Solving
1 + 2y = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2y = 0 + -1
2y = 0 + -1

Combine like terms: 0 + -1 = -1
2y = -1

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Solution
y = {-5, -0.5}