a*a+1+6a*a+8a=0

Solution for a*a+1+6a*a+8a=0 equation:

Simplifying
a * a + 1 + 6a * a + 8a = 0

Multiply a * a
a2 + 1 + 6a * a + 8a = 0

Multiply a * a
a2 + 1 + 6a2 + 8a = 0

Reorder the terms:
1 + 8a + a2 + 6a2 = 0

Combine like terms: a2 + 6a2 = 7a2
1 + 8a + 7a2 = 0

Solving
1 + 8a + 7a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(1 + a)(1 + 7a) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + 7a)' equal to zero and attempt to solve:

Simplifying
1 + 7a = 0

Solving
1 + 7a = 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 + 7a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7a = 0 + -1
7a = 0 + -1

Combine like terms: 0 + -1 = -1
7a = -1

Divide each side by '7'.
a = -0.1428571429

Simplifying
a = -0.1428571429
Solution
a = {-1, -0.1428571429}