(3y-1)(4+y)=0

Solution for (3y-1)(4+y)=0 equation:

Simplifying
(3y + -1)(4 + y) = 0

Reorder the terms:
(-1 + 3y)(4 + y) = 0

Multiply (-1 + 3y) * (4 + y)
(-1(4 + y) + 3y * (4 + y)) = 0
((4 * -1 + y * -1) + 3y * (4 + y)) = 0
((-4 + -1y) + 3y * (4 + y)) = 0
(-4 + -1y + (4 * 3y + y * 3y)) = 0
(-4 + -1y + (12y + 3y2)) = 0

Combine like terms: -1y + 12y = 11y
(-4 + 11y + 3y2) = 0

Solving
-4 + 11y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-4 + -1y)(1 + -3y) = 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 + -3y)' equal to zero and attempt to solve:

Simplifying
1 + -3y = 0

Solving
1 + -3y = 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 + -3y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3y = 0 + -1
-3y = 0 + -1

Combine like terms: 0 + -1 = -1
-3y = -1

Divide each side by '-3'.
y = 0.3333333333

Simplifying
y = 0.3333333333
Solution
y = {-4, 0.3333333333}