100a-a^2+309=0

Solution for 100a-a^2+309=0 equation:

Simplifying
100a + -1a2 + 309 = 0

Reorder the terms:
309 + 100a + -1a2 = 0

Solving
309 + 100a + -1a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(103 + -1a)(3 + a) = 0

Subproblem 1
Set the factor '(103 + -1a)' equal to zero and attempt to solve:

Simplifying
103 + -1a = 0

Solving
103 + -1a = 0

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

Add '-103' to each side of the equation.
103 + -103 + -1a = 0 + -103

Combine like terms: 103 + -103 = 0
0 + -1a = 0 + -103
-1a = 0 + -103

Combine like terms: 0 + -103 = -103
-1a = -103

Divide each side by '-1'.
a = 103

Simplifying
a = 103
Subproblem 2
Set the factor '(3 + a)' equal to zero and attempt to solve:

Simplifying
3 + a = 0

Solving
3 + a = 0

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

Add '-3' to each side of the equation.
3 + -3 + a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + a = 0 + -3
a = 0 + -3

Combine like terms: 0 + -3 = -3
a = -3

Simplifying
a = -3
Solution
a = {103, -3}