a(a+12)=a

Solution for a(a+12)=a equation:

Simplifying
a(a + 12) = a

Reorder the terms:
a(12 + a) = a
(12 * a + a * a) = a
(12a + a2) = a

Solving
12a + a2 = a

Solving for variable 'a'.

Reorder the terms:
12a + -1a + a2 = a + -1a

Combine like terms: 12a + -1a = 11a
11a + a2 = a + -1a

Combine like terms: a + -1a = 0
11a + a2 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(11 + a) = 0

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(11 + a)' equal to zero and attempt to solve:

Simplifying
11 + a = 0

Solving
11 + a = 0

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

Add '-11' to each side of the equation.
11 + -11 + a = 0 + -11

Combine like terms: 11 + -11 = 0
0 + a = 0 + -11
a = 0 + -11

Combine like terms: 0 + -11 = -11
a = -11

Simplifying
a = -11
Solution
a = {0, -11}