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

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

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

Reorder the terms:
y(4 + y) + -3(y + 4) = 0
(4 * y + y * y) + -3(y + 4) = 0
(4y + y2) + -3(y + 4) = 0

Reorder the terms:
4y + y2 + -3(4 + y) = 0
4y + y2 + (4 * -3 + y * -3) = 0
4y + y2 + (-12 + -3y) = 0

Reorder the terms:
-12 + 4y + -3y + y2 = 0

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

Solving
-12 + 1y + y2 = 0

Solving for variable 'y'.

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

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

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

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

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-4, 3}