6a^2-8ab-14b^2=0

Solution for 6a^2-8ab-14b^2=0 equation:

Simplifying
6a2 + -8ab + -14b2 = 0

Reorder the terms:
-8ab + 6a2 + -14b2 = 0

Solving
-8ab + 6a2 + -14b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4ab + 3a2 + -7b2) = 0

Factor a trinomial.
2((3a + -7b)(a + b)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3a + -7b)' equal to zero and attempt to solve:

Simplifying
3a + -7b = 0

Solving
3a + -7b = 0

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

Add '7b' to each side of the equation.
3a + -7b + 7b = 0 + 7b

Combine like terms: -7b + 7b = 0
3a + 0 = 0 + 7b
3a = 0 + 7b
Remove the zero:
3a = 7b

Divide each side by '3'.
a = 2.333333333b

Simplifying
a = 2.333333333b
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 = {2.333333333b, -1b}