a^2+6a=55

Solution for a^2+6a=55 equation:

Simplifying
a2 + 6a = 55

Reorder the terms:
6a + a2 = 55

Solving
6a + a2 = 55

Solving for variable 'a'.

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

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

Factor a trinomial.
(-11 + -1a)(5 + -1a) = 0

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

Simplifying
-11 + -1a = 0

Solving
-11 + -1a = 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 + -1a = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1a = 0 + 11
-1a = 0 + 11

Combine like terms: 0 + 11 = 11
-1a = 11

Divide each side by '-1'.
a = -11

Simplifying
a = -11
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 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 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

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