y(y+5)=2y

Solution for y(y+5)=2y equation:

Simplifying
y(y + 5) = 2y

Reorder the terms:
y(5 + y) = 2y
(5 * y + y * y) = 2y
(5y + y2) = 2y

Solving
5y + y2 = 2y

Solving for variable 'y'.

Reorder the terms:
5y + -2y + y2 = 2y + -2y

Combine like terms: 5y + -2y = 3y
3y + y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
3y + y2 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(3 + 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 '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

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

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

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

Simplifying
y = -3
Solution
y = {0, -3}