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

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

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

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

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

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

Solving
1 + 2y + -8y2 = 0

Solving for variable 'y'.

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

Subproblem 1
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
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 = {0.5, -0.25}