a^2+8=-6a

Solution for a^2+8=-6a equation:

Simplifying
a2 + 8 = -6a

Reorder the terms:
8 + a2 = -6a

Solving
8 + a2 = -6a

Solving for variable 'a'.

Reorder the terms:
8 + 6a + a2 = -6a + 6a

Combine like terms: -6a + 6a = 0
8 + 6a + a2 = 0

Factor a trinomial.
(4 + a)(2 + a) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(2 + a)' equal to zero and attempt to solve:

Simplifying
2 + a = 0

Solving
2 + a = 0

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

Add '-2' to each side of the equation.
2 + -2 + a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + a = 0 + -2
a = 0 + -2

Combine like terms: 0 + -2 = -2
a = -2

Simplifying
a = -2
Solution
a = {-4, -2}