-204+29a-a^2=0

Solution for -204+29a-a^2=0 equation:

Simplifying
-204 + 29a + -1a2 = 0

Solving
-204 + 29a + -1a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-17 + a)(12 + -1a) = 0

Subproblem 1
Set the factor '(-17 + a)' equal to zero and attempt to solve:

Simplifying
-17 + a = 0

Solving
-17 + a = 0

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

Add '17' to each side of the equation.
-17 + 17 + a = 0 + 17

Combine like terms: -17 + 17 = 0
0 + a = 0 + 17
a = 0 + 17

Combine like terms: 0 + 17 = 17
a = 17

Simplifying
a = 17
Subproblem 2
Set the factor '(12 + -1a)' equal to zero and attempt to solve:

Simplifying
12 + -1a = 0

Solving
12 + -1a = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1a = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1a = 0 + -12
-1a = 0 + -12

Combine like terms: 0 + -12 = -12
-1a = -12

Divide each side by '-1'.
a = 12

Simplifying
a = 12
Solution
a = {17, 12}