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

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

Simplifying
ax + -6a2 + x2 = 0

Solving
ax + -6a2 + x2 = 0

Solving for variable 'a'.

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

Subproblem 1
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
Subproblem 2
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
Solution
a = {-0.3333333333x, 0.5x}