15a^2-13ab+2b^2=0

Solution for 15a^2-13ab+2b^2=0 equation:

Simplifying
15a2 + -13ab + 2b2 = 0

Reorder the terms:
-13ab + 15a2 + 2b2 = 0

Solving
-13ab + 15a2 + 2b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3a + -2b)(5a + -1b) = 0

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

Simplifying
3a + -2b = 0

Solving
3a + -2b = 0

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

Add '2b' to each side of the equation.
3a + -2b + 2b = 0 + 2b

Combine like terms: -2b + 2b = 0
3a + 0 = 0 + 2b
3a = 0 + 2b
Remove the zero:
3a = 2b

Divide each side by '3'.
a = 0.6666666667b

Simplifying
a = 0.6666666667b
Subproblem 2
Set the factor '(5a + -1b)' equal to zero and attempt to solve:

Simplifying
5a + -1b = 0

Solving
5a + -1b = 0

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

Add 'b' to each side of the equation.
5a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
5a + 0 = 0 + b
5a = 0 + b
Remove the zero:
5a = b

Divide each side by '5'.
a = 0.2b

Simplifying
a = 0.2b
Solution
a = {0.6666666667b, 0.2b}