=a^2+11a+30

Solution for =a^2+11a+30 equation:

Simplifying
0 = a2 + 11a + 30

Reorder the terms:
0 = 30 + 11a + a2

Solving
0 = 30 + 11a + a2

Solving for variable 'a'.

Combine like terms: 0 + -30 = -30
-30 + -11a + -1a2 = 30 + 11a + a2 + -30 + -11a + -1a2

Reorder the terms:
-30 + -11a + -1a2 = 30 + -30 + 11a + -11a + a2 + -1a2

Combine like terms: 30 + -30 = 0
-30 + -11a + -1a2 = 0 + 11a + -11a + a2 + -1a2
-30 + -11a + -1a2 = 11a + -11a + a2 + -1a2

Combine like terms: 11a + -11a = 0
-30 + -11a + -1a2 = 0 + a2 + -1a2
-30 + -11a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-30 + -11a + -1a2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(30 + 11a + a2) = 0

Factor a trinomial.
-1((6 + a)(5 + a)) = 0

Ignore the factor -1.
Subproblem 1
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
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 = {-6, -5}