a^2-16a+45=6

Solution for a^2-16a+45=6 equation:

Simplifying
a2 + -16a + 45 = 6

Reorder the terms:
45 + -16a + a2 = 6

Solving
45 + -16a + a2 = 6

Solving for variable 'a'.

Reorder the terms:
45 + -6 + -16a + a2 = 6 + -6

Combine like terms: 45 + -6 = 39
39 + -16a + a2 = 6 + -6

Combine like terms: 6 + -6 = 0
39 + -16a + a2 = 0

Factor a trinomial.
(3 + -1a)(13 + -1a) = 0

Subproblem 1
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Subproblem 2
Set the factor '(13 + -1a)' equal to zero and attempt to solve:

Simplifying
13 + -1a = 0

Solving
13 + -1a = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1a = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1a = 0 + -13
-1a = 0 + -13

Combine like terms: 0 + -13 = -13
-1a = -13

Divide each side by '-1'.
a = 13

Simplifying
a = 13
Solution
a = {3, 13}