0=-a^2+29a-204

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

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

Reorder the terms:
0 = -204 + 29a + -1a2

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

Solving for variable 'a'.

Combine like terms: 0 + 204 = 204
204 + -29a + a2 = -204 + 29a + -1a2 + 204 + -29a + a2

Reorder the terms:
204 + -29a + a2 = -204 + 204 + 29a + -29a + -1a2 + a2

Combine like terms: -204 + 204 = 0
204 + -29a + a2 = 0 + 29a + -29a + -1a2 + a2
204 + -29a + a2 = 29a + -29a + -1a2 + a2

Combine like terms: 29a + -29a = 0
204 + -29a + a2 = 0 + -1a2 + a2
204 + -29a + a2 = -1a2 + a2

Combine like terms: -1a2 + a2 = 0
204 + -29a + a2 = 0

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

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

Simplifying
17 + -1a = 0

Solving
17 + -1a = 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 + -1a = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1a = 0 + -17
-1a = 0 + -17

Combine like terms: 0 + -17 = -17
-1a = -17

Divide each side by '-1'.
a = 17

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