0=a(a+6)

Solution for 0=a(a+6) equation:

Simplifying
0 = a(a + 6)

Reorder the terms:
0 = a(6 + a)
0 = (6 * a + a * a)
0 = (6a + a2)

Solving
0 = 6a + a2

Solving for variable 'a'.
Remove the zero:
-6a + -1a2 = 6a + a2 + -6a + -1a2

Reorder the terms:
-6a + -1a2 = 6a + -6a + a2 + -1a2

Combine like terms: 6a + -6a = 0
-6a + -1a2 = 0 + a2 + -1a2
-6a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-6a + -1a2 = 0

Factor out the Greatest Common Factor (GCF), '-1a'.
-1a(6 + a) = 0

Ignore the factor -1.
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 '(6 + a)' equal to zero and attempt to solve:

Simplifying
6 + a = 0

Solving
6 + a = 0

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

Add '-6' to each side of the equation.
6 + -6 + a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + a = 0 + -6
a = 0 + -6

Combine like terms: 0 + -6 = -6
a = -6

Simplifying
a = -6
Solution
a = {0, -6}