2x^2-13ax+15a^2=0

Solution for 2x^2-13ax+15a^2=0 equation:

Simplifying
2x2 + -13ax + 15a2 = 0

Reorder the terms:
-13ax + 15a2 + 2x2 = 0

Solving
-13ax + 15a2 + 2x2 = 0

Solving for variable 'a'.

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

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

Simplifying
3a + -2x = 0

Solving
3a + -2x = 0

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

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

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

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

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

Simplifying
5a + -1x = 0

Solving
5a + -1x = 0

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

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

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

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

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