a^2-13a+19=7

Solution for a^2-13a+19=7 equation:

Simplifying
a2 + -13a + 19 = 7

Reorder the terms:
19 + -13a + a2 = 7

Solving
19 + -13a + a2 = 7

Solving for variable 'a'.

Reorder the terms:
19 + -7 + -13a + a2 = 7 + -7

Combine like terms: 19 + -7 = 12
12 + -13a + a2 = 7 + -7

Combine like terms: 7 + -7 = 0
12 + -13a + a2 = 0

Factor a trinomial.
(1 + -1a)(12 + -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 '(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 = {1, 12}