a^2+6=-7a

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

Simplifying
a2 + 6 = -7a

Reorder the terms:
6 + a2 = -7a

Solving
6 + a2 = -7a

Solving for variable 'a'.

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

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

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

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 '(1 + a)' equal to zero and attempt to solve:

Simplifying
1 + a = 0

Solving
1 + a = 0

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

Add '-1' to each side of the equation.
1 + -1 + a = 0 + -1

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

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

Simplifying
a = -1
Solution
a = {-6, -1}