-a^2=100-20a

Solution for -a^2=100-20a equation:

Simplifying
-1a2 = 100 + -20a

Solving
-1a2 = 100 + -20a

Solving for variable 'a'.

Reorder the terms:
-100 + 20a + -1a2 = 100 + -20a + -100 + 20a

Reorder the terms:
-100 + 20a + -1a2 = 100 + -100 + -20a + 20a

Combine like terms: 100 + -100 = 0
-100 + 20a + -1a2 = 0 + -20a + 20a
-100 + 20a + -1a2 = -20a + 20a

Combine like terms: -20a + 20a = 0
-100 + 20a + -1a2 = 0

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

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

Simplifying
-10 + a = 0

Solving
-10 + a = 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 + a = 0 + 10

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

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

Simplifying
a = 10
Subproblem 2
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
Solution
a = {10, 10}