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

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

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

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

Multiply (2 + y) * (1 + 4y)
(2(1 + 4y) + y(1 + 4y)) = 0
((1 * 2 + 4y * 2) + y(1 + 4y)) = 0
((2 + 8y) + y(1 + 4y)) = 0
(2 + 8y + (1 * y + 4y * y)) = 0
(2 + 8y + (1y + 4y2)) = 0

Combine like terms: 8y + 1y = 9y
(2 + 9y + 4y2) = 0

Solving
2 + 9y + 4y2 = 0

Solving for variable 'y'.

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

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

Simplifying
2 + y = 0

Solving
2 + y = 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 + y = 0 + -2

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

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

Simplifying
y = -2
Subproblem 2
Set the factor '(1 + 4y)' equal to zero and attempt to solve:

Simplifying
1 + 4y = 0

Solving
1 + 4y = 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 + 4y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4y = 0 + -1
4y = 0 + -1

Combine like terms: 0 + -1 = -1
4y = -1

Divide each side by '4'.
y = -0.25

Simplifying
y = -0.25
Solution
y = {-2, -0.25}