x^2-cx-6c^2=0

Solution for x^2-cx-6c^2=0 equation:

Simplifying
x2 + -1cx + -6c2 = 0

Reorder the terms:
-1cx + -6c2 + x2 = 0

Solving
-1cx + -6c2 + x2 = 0

Solving for variable 'c'.

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

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

Simplifying
-2c + -1x = 0

Solving
-2c + -1x = 0

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

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

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

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

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

Simplifying
3c + -1x = 0

Solving
3c + -1x = 0

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

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

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

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

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