a^2=13a-42

Solution for a^2=13a-42 equation:

Simplifying
a2 = 13a + -42

Reorder the terms:
a2 = -42 + 13a

Solving
a2 = -42 + 13a

Solving for variable 'a'.

Reorder the terms:
42 + -13a + a2 = -42 + 13a + 42 + -13a

Reorder the terms:
42 + -13a + a2 = -42 + 42 + 13a + -13a

Combine like terms: -42 + 42 = 0
42 + -13a + a2 = 0 + 13a + -13a
42 + -13a + a2 = 13a + -13a

Combine like terms: 13a + -13a = 0
42 + -13a + a2 = 0

Factor a trinomial.
(6 + -1a)(7 + -1a) = 0

Subproblem 1
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Subproblem 2
Set the factor '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {6, 7}