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

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

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

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

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

Combine like terms: -1y + 8y = 7y
(2 + 7y + -4y2) = 0

Solving
2 + 7y + -4y2 = 0

Solving for variable 'y'.

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

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

Simplifying
2 + -1y = 0

Solving
2 + -1y = 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 + -1y = 0 + -2

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

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

Divide each side by '-1'.
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}