3b^2-3a^2+ab-9ab=0

Solution for 3b^2-3a^2+ab-9ab=0 equation:

Simplifying
3b2 + -3a2 + ab + -9ab = 0

Reorder the terms:
ab + -9ab + -3a2 + 3b2 = 0

Combine like terms: ab + -9ab = -8ab
-8ab + -3a2 + 3b2 = 0

Solving
-8ab + -3a2 + 3b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1a + -3b)(3a + -1b) = 0

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

Simplifying
-1a + -3b = 0

Solving
-1a + -3b = 0

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

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

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

Divide each side by '-1'.
a = -3b

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

Simplifying
3a + -1b = 0

Solving
3a + -1b = 0

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

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

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

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

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