8a^2-80a+200=0

Solution for 8a^2-80a+200=0 equation:

Simplifying
8a2 + -80a + 200 = 0

Reorder the terms:
200 + -80a + 8a2 = 0

Solving
200 + -80a + 8a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '8'.
8(25 + -10a + a2) = 0

Factor a trinomial.
8((5 + -1a)(5 + -1a)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 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 + -1a = 0 + -5

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

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

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 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 + -1a = 0 + -5

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

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

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {5, 5}