4(y+5)(2y+1)=0

Solution for 4(y+5)(2y+1)=0 equation:

Simplifying
4(y + 5)(2y + 1) = 0

Reorder the terms:
4(5 + y)(2y + 1) = 0

Reorder the terms:
4(5 + y)(1 + 2y) = 0

Multiply (5 + y) * (1 + 2y)
4(5(1 + 2y) + y(1 + 2y)) = 0
4((1 * 5 + 2y * 5) + y(1 + 2y)) = 0
4((5 + 10y) + y(1 + 2y)) = 0
4(5 + 10y + (1 * y + 2y * y)) = 0
4(5 + 10y + (1y + 2y2)) = 0

Combine like terms: 10y + 1y = 11y
4(5 + 11y + 2y2) = 0
(5 * 4 + 11y * 4 + 2y2 * 4) = 0
(20 + 44y + 8y2) = 0

Solving
20 + 44y + 8y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + 11y + 2y2) = 0

Factor a trinomial.
4((5 + y)(1 + 2y)) = 0

Ignore the factor 4.
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}