a^2+28=-11a

Solution for a^2+28=-11a equation:

Simplifying
a2 + 28 = -11a

Reorder the terms:
28 + a2 = -11a

Solving
28 + a2 = -11a

Solving for variable 'a'.

Reorder the terms:
28 + 11a + a2 = -11a + 11a

Combine like terms: -11a + 11a = 0
28 + 11a + a2 = 0

Factor a trinomial.
(7 + a)(4 + 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 '(4 + a)' equal to zero and attempt to solve:

Simplifying
4 + a = 0

Solving
4 + a = 0

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

Add '-4' to each side of the equation.
4 + -4 + a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + a = 0 + -4
a = 0 + -4

Combine like terms: 0 + -4 = -4
a = -4

Simplifying
a = -4
Solution
a = {-7, -4}