-a^2=64-16a

Solution for -a^2=64-16a equation:

Simplifying
-1a2 = 64 + -16a

Solving
-1a2 = 64 + -16a

Solving for variable 'a'.

Reorder the terms:
-64 + 16a + -1a2 = 64 + -16a + -64 + 16a

Reorder the terms:
-64 + 16a + -1a2 = 64 + -64 + -16a + 16a

Combine like terms: 64 + -64 = 0
-64 + 16a + -1a2 = 0 + -16a + 16a
-64 + 16a + -1a2 = -16a + 16a

Combine like terms: -16a + 16a = 0
-64 + 16a + -1a2 = 0

Factor a trinomial.
(-8 + a)(8 + -1a) = 0

Subproblem 1
Set the factor '(-8 + a)' equal to zero and attempt to solve:

Simplifying
-8 + a = 0

Solving
-8 + a = 0

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

Add '8' to each side of the equation.
-8 + 8 + a = 0 + 8

Combine like terms: -8 + 8 = 0
0 + a = 0 + 8
a = 0 + 8

Combine like terms: 0 + 8 = 8
a = 8

Simplifying
a = 8
Subproblem 2
Set the factor '(8 + -1a)' equal to zero and attempt to solve:

Simplifying
8 + -1a = 0

Solving
8 + -1a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1a = 0 + -8
-1a = 0 + -8

Combine like terms: 0 + -8 = -8
-1a = -8

Divide each side by '-1'.
a = 8

Simplifying
a = 8
Solution
a = {8, 8}