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

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

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

Reorder the terms:
y(1 + y) + -3y = y + y
(1 * y + y * y) + -3y = y + y
(1y + y2) + -3y = y + y

Reorder the terms:
1y + -3y + y2 = y + y

Combine like terms: 1y + -3y = -2y
-2y + y2 = y + y

Combine like terms: y + y = 2y
-2y + y2 = 2y

Solving
-2y + y2 = 2y

Solving for variable 'y'.

Reorder the terms:
-2y + -2y + y2 = 2y + -2y

Combine like terms: -2y + -2y = -4y
-4y + y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
-4y + y2 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-4 + y) = 0

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(-4 + y)' equal to zero and attempt to solve:

Simplifying
-4 + y = 0

Solving
-4 + y = 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 + y = 0 + 4

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

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

Simplifying
y = 4
Solution
y = {0, 4}