8a^2+65ab+8b^2=0

Solution for 8a^2+65ab+8b^2=0 equation:

Simplifying
8a2 + 65ab + 8b2 = 0

Reorder the terms:
65ab + 8a2 + 8b2 = 0

Solving
65ab + 8a2 + 8b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(8a + b)(a + 8b) = 0

Subproblem 1
Set the factor '(8a + b)' equal to zero and attempt to solve:

Simplifying
8a + b = 0

Solving
8a + b = 0

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

Add '-1b' to each side of the equation.
8a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
8a + 0 = 0 + -1b
8a = 0 + -1b
Remove the zero:
8a = -1b

Divide each side by '8'.
a = -0.125b

Simplifying
a = -0.125b
Subproblem 2
Set the factor '(a + 8b)' equal to zero and attempt to solve:

Simplifying
a + 8b = 0

Solving
a + 8b = 0

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

Add '-8b' to each side of the equation.
a + 8b + -8b = 0 + -8b

Combine like terms: 8b + -8b = 0
a + 0 = 0 + -8b
a = 0 + -8b
Remove the zero:
a = -8b

Simplifying
a = -8b
Solution
a = {-0.125b, -8b}