a(a+2)=120

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

Simplifying
a(a + 2) = 120

Reorder the terms:
a(2 + a) = 120
(2 * a + a * a) = 120
(2a + a2) = 120

Solving
2a + a2 = 120

Solving for variable 'a'.

Reorder the terms:
-120 + 2a + a2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 2a + a2 = 0

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

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

Simplifying
-12 + -1a = 0

Solving
-12 + -1a = 0

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

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

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

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

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

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

Simplifying
10 + -1a = 0

Solving
10 + -1a = 0

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

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

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

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

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

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