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

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

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

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

Multiply (4 + y) * (-1 + 4y)
(4(-1 + 4y) + y(-1 + 4y)) = 0
((-1 * 4 + 4y * 4) + y(-1 + 4y)) = 0
((-4 + 16y) + y(-1 + 4y)) = 0
(-4 + 16y + (-1 * y + 4y * y)) = 0
(-4 + 16y + (-1y + 4y2)) = 0

Combine like terms: 16y + -1y = 15y
(-4 + 15y + 4y2) = 0

Solving
-4 + 15y + 4y2 = 0

Solving for variable 'y'.

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

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

Simplifying
-4 + -1y = 0

Solving
-4 + -1y = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1y = 0 + 4

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

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

Divide each side by '-1'.
y = -4

Simplifying
y = -4
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 = {-4, 0.25}