a^2-12a+6=13+6

Solution for a^2-12a+6=13+6 equation:

Simplifying
a2 + -12a + 6 = 13 + 6

Reorder the terms:
6 + -12a + a2 = 13 + 6

Combine like terms: 13 + 6 = 19
6 + -12a + a2 = 19

Solving
6 + -12a + a2 = 19

Solving for variable 'a'.

Reorder the terms:
6 + -19 + -12a + a2 = 19 + -19

Combine like terms: 6 + -19 = -13
-13 + -12a + a2 = 19 + -19

Combine like terms: 19 + -19 = 0
-13 + -12a + a2 = 0

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

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

Simplifying
-1 + -1a = 0

Solving
-1 + -1a = 0

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

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

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

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

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

Simplifying
a = -1
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 = {-1, 13}