-6a^2-6b^2+20ab=0

Solution for -6a^2-6b^2+20ab=0 equation:

Simplifying
-6a2 + -6b2 + 20ab = 0

Reorder the terms:
20ab + -6a2 + -6b2 = 0

Solving
20ab + -6a2 + -6b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10ab + -3a2 + -3b2) = 0

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

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

Simplifying
-3a + b = 0

Solving
-3a + b = 0

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

Add '-1b' to each side of the equation.
-3a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
-3a + 0 = 0 + -1b
-3a = 0 + -1b
Remove the zero:
-3a = -1b

Divide each side by '-3'.
a = 0.3333333333b

Simplifying
a = 0.3333333333b
Subproblem 2
Set the factor '(a + -3b)' equal to zero and attempt to solve:

Simplifying
a + -3b = 0

Solving
a + -3b = 0

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

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

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

Simplifying
a = 3b
Solution
a = {0.3333333333b, 3b}