a^2=-42-13a

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

Simplifying
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.
(7 + a)(6 + a) = 0

Subproblem 1
Set the factor '(7 + a)' equal to zero and attempt to solve:

Simplifying
7 + a = 0

Solving
7 + a = 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 + a = 0 + -7

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

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

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

Simplifying
6 + a = 0

Solving
6 + a = 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 + a = 0 + -6

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

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

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