y(y+2)=120

Solution for y(y+2)=120 equation:

Simplifying
y(y + 2) = 120

Reorder the terms:
y(2 + y) = 120
(2 * y + y * y) = 120
(2y + y2) = 120

Solving
2y + y2 = 120

Solving for variable 'y'.

Reorder the terms:
-120 + 2y + y2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 2y + y2 = 0

Factor a trinomial.
(-12 + -1y)(10 + -1y) = 0

Subproblem 1
Set the factor '(-12 + -1y)' equal to zero and attempt to solve:

Simplifying
-12 + -1y = 0

Solving
-12 + -1y = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1y = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1y = 0 + 12
-1y = 0 + 12

Combine like terms: 0 + 12 = 12
-1y = 12

Divide each side by '-1'.
y = -12

Simplifying
y = -12
Subproblem 2
Set the factor '(10 + -1y)' equal to zero and attempt to solve:

Simplifying
10 + -1y = 0

Solving
10 + -1y = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1y = 0 + -10
-1y = 0 + -10

Combine like terms: 0 + -10 = -10
-1y = -10

Divide each side by '-1'.
y = 10

Simplifying
y = 10
Solution
y = {-12, 10}