x^2-ax-6a^2=0

Solution for x^2-ax-6a^2=0 equation:

Simplifying
x2 + -1ax + -6a2 = 0

Reorder the terms:
-1ax + -6a2 + x2 = 0

Solving
-1ax + -6a2 + x2 = 0

Solving for variable 'a'.

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

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

Simplifying
-2a + -1x = 0

Solving
-2a + -1x = 0

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

Add 'x' to each side of the equation.
-2a + -1x + x = 0 + x

Combine like terms: -1x + x = 0
-2a + 0 = 0 + x
-2a = 0 + x
Remove the zero:
-2a = x

Divide each side by '-2'.
a = -0.5x

Simplifying
a = -0.5x
Subproblem 2
Set the factor '(3a + -1x)' equal to zero and attempt to solve:

Simplifying
3a + -1x = 0

Solving
3a + -1x = 0

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

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

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

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

Simplifying
a = 0.3333333333x
Solution
a = {-0.5x, 0.3333333333x}