a^2+9a+61=6-7a

Solution for a^2+9a+61=6-7a equation:

Simplifying
a2 + 9a + 61 = 6 + -7a

Reorder the terms:
61 + 9a + a2 = 6 + -7a

Solving
61 + 9a + a2 = 6 + -7a

Solving for variable 'a'.

Reorder the terms:
61 + -6 + 9a + 7a + a2 = 6 + -7a + -6 + 7a

Combine like terms: 61 + -6 = 55
55 + 9a + 7a + a2 = 6 + -7a + -6 + 7a

Combine like terms: 9a + 7a = 16a
55 + 16a + a2 = 6 + -7a + -6 + 7a

Reorder the terms:
55 + 16a + a2 = 6 + -6 + -7a + 7a

Combine like terms: 6 + -6 = 0
55 + 16a + a2 = 0 + -7a + 7a
55 + 16a + a2 = -7a + 7a

Combine like terms: -7a + 7a = 0
55 + 16a + a2 = 0

Factor a trinomial.
(11 + a)(5 + a) = 0

Subproblem 1
Set the factor '(11 + a)' equal to zero and attempt to solve:

Simplifying
11 + a = 0

Solving
11 + a = 0

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

Add '-11' to each side of the equation.
11 + -11 + a = 0 + -11

Combine like terms: 11 + -11 = 0
0 + a = 0 + -11
a = 0 + -11

Combine like terms: 0 + -11 = -11
a = -11

Simplifying
a = -11
Subproblem 2
Set the factor '(5 + a)' equal to zero and attempt to solve:

Simplifying
5 + a = 0

Solving
5 + a = 0

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

Add '-5' to each side of the equation.
5 + -5 + a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + a = 0 + -5
a = 0 + -5

Combine like terms: 0 + -5 = -5
a = -5

Simplifying
a = -5
Solution
a = {-11, -5}