6a^2-2ab-8b^2=0

Solution for 6a^2-2ab-8b^2=0 equation:

Simplifying
6a2 + -2ab + -8b2 = 0

Reorder the terms:
-2ab + 6a2 + -8b2 = 0

Solving
-2ab + 6a2 + -8b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1ab + 3a2 + -4b2) = 0

Factor a trinomial.
2((3a + -4b)(a + b)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3a + -4b)' equal to zero and attempt to solve:

Simplifying
3a + -4b = 0

Solving
3a + -4b = 0

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

Add '4b' to each side of the equation.
3a + -4b + 4b = 0 + 4b

Combine like terms: -4b + 4b = 0
3a + 0 = 0 + 4b
3a = 0 + 4b
Remove the zero:
3a = 4b

Divide each side by '3'.
a = 1.333333333b

Simplifying
a = 1.333333333b
Subproblem 2
Set the factor '(a + b)' equal to zero and attempt to solve:

Simplifying
a + b = 0

Solving
a + b = 0

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

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

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

Simplifying
a = -1b
Solution
a = {1.333333333b, -1b}