12a^2-9ab-21b^2=0

Solution for 12a^2-9ab-21b^2=0 equation:

Simplifying
12a2 + -9ab + -21b2 = 0

Reorder the terms:
-9ab + 12a2 + -21b2 = 0

Solving
-9ab + 12a2 + -21b2 = 0

Solving for variable 'a'.

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

Factor a trinomial.
3((4a + -7b)(a + b)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4a + -7b)' equal to zero and attempt to solve:

Simplifying
4a + -7b = 0

Solving
4a + -7b = 0

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

Add '7b' to each side of the equation.
4a + -7b + 7b = 0 + 7b

Combine like terms: -7b + 7b = 0
4a + 0 = 0 + 7b
4a = 0 + 7b
Remove the zero:
4a = 7b

Divide each side by '4'.
a = 1.75b

Simplifying
a = 1.75b
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 = {1.75b, -1b}