32a=-a^2

Solution for 32a=-a^2 equation:

Simplifying
32a = -1a2

Solving
32a = -1a2

Solving for variable 'a'.

Combine like terms: -1a2 + a2 = 0
32a + a2 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(32 + 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 '(32 + a)' equal to zero and attempt to solve:

Simplifying
32 + a = 0

Solving
32 + a = 0

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

Add '-32' to each side of the equation.
32 + -32 + a = 0 + -32

Combine like terms: 32 + -32 = 0
0 + a = 0 + -32
a = 0 + -32

Combine like terms: 0 + -32 = -32
a = -32

Simplifying
a = -32
Solution
a = {0, -32}