15a^2-3ab-18b^2=0

Solution for 15a^2-3ab-18b^2=0 equation:

Simplifying
15a2 + -3ab + -18b2 = 0

Reorder the terms:
-3ab + 15a2 + -18b2 = 0

Solving
-3ab + 15a2 + -18b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1ab + 5a2 + -6b2) = 0

Factor a trinomial.
3((5a + -6b)(a + b)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5a + -6b)' equal to zero and attempt to solve:

Simplifying
5a + -6b = 0

Solving
5a + -6b = 0

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

Add '6b' to each side of the equation.
5a + -6b + 6b = 0 + 6b

Combine like terms: -6b + 6b = 0
5a + 0 = 0 + 6b
5a = 0 + 6b
Remove the zero:
5a = 6b

Divide each side by '5'.
a = 1.2b

Simplifying
a = 1.2b
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 = {1.2b, -1b}