a^2=-6a

Solution for a^2=-6a equation:

Simplifying
a2 = -6a

Solving
a2 = -6a

Solving for variable 'a'.

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

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

Factor out the Greatest Common Factor (GCF), 'a'.
a(6 + 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 '(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}