39a=-a^2

Solution for 39a=-a^2 equation:

Simplifying
39a = -1a2

Solving
39a = -1a2

Solving for variable 'a'.

Combine like terms: -1a2 + a2 = 0
39a + a2 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(39 + 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 '(39 + a)' equal to zero and attempt to solve:

Simplifying
39 + a = 0

Solving
39 + a = 0

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

Add '-39' to each side of the equation.
39 + -39 + a = 0 + -39

Combine like terms: 39 + -39 = 0
0 + a = 0 + -39
a = 0 + -39

Combine like terms: 0 + -39 = -39
a = -39

Simplifying
a = -39
Solution
a = {0, -39}