5a^2=65a-200

Solution for 5a^2=65a-200 equation:

Simplifying
5a2 = 65a + -200

Reorder the terms:
5a2 = -200 + 65a

Solving
5a2 = -200 + 65a

Solving for variable 'a'.

Reorder the terms:
200 + -65a + 5a2 = -200 + 65a + 200 + -65a

Reorder the terms:
200 + -65a + 5a2 = -200 + 200 + 65a + -65a

Combine like terms: -200 + 200 = 0
200 + -65a + 5a2 = 0 + 65a + -65a
200 + -65a + 5a2 = 65a + -65a

Combine like terms: 65a + -65a = 0
200 + -65a + 5a2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(40 + -13a + a2) = 0

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

Ignore the factor 5.
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 '(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 = {5, 8}