-a^2+50=-5a

Solution for -a^2+50=-5a equation:

Simplifying
-1a2 + 50 = -5a

Reorder the terms:
50 + -1a2 = -5a

Solving
50 + -1a2 = -5a

Solving for variable 'a'.

Reorder the terms:
50 + 5a + -1a2 = -5a + 5a

Combine like terms: -5a + 5a = 0
50 + 5a + -1a2 = 0

Factor a trinomial.
(10 + -1a)(5 + a) = 0

Subproblem 1
Set the factor '(10 + -1a)' equal to zero and attempt to solve:

Simplifying
10 + -1a = 0

Solving
10 + -1a = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1a = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1a = 0 + -10
-1a = 0 + -10

Combine like terms: 0 + -10 = -10
-1a = -10

Divide each side by '-1'.
a = 10

Simplifying
a = 10
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 = {10, -5}