-a^2=4a+a

Solution for -a^2=4a+a equation:

Simplifying
-1a2 = 4a + a

Combine like terms: 4a + a = 5a
-1a2 = 5a

Solving
-1a2 = 5a

Solving for variable 'a'.

Reorder the terms:
-5a + -1a2 = 5a + -5a

Combine like terms: 5a + -5a = 0
-5a + -1a2 = 0

Factor out the Greatest Common Factor (GCF), '-1a'.
-1a(5 + 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 '(5 + a)' equal to zero and attempt to solve:

Simplifying
5 + a = 0

Solving
5 + a = 0

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

Add '-5' to each side of the equation.
5 + -5 + a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + a = 0 + -5
a = 0 + -5

Combine like terms: 0 + -5 = -5
a = -5

Simplifying
a = -5
Solution
a = {0, -5}