x^2-2ax-3a^2=0

Solution for x^2-2ax-3a^2=0 equation:

Simplifying
x2 + -2ax + -3a2 = 0

Reorder the terms:
-2ax + -3a2 + x2 = 0

Solving
-2ax + -3a2 + x2 = 0

Solving for variable 'a'.

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

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

Simplifying
-1a + -1x = 0

Solving
-1a + -1x = 0

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

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

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

Divide each side by '-1'.
a = -1x

Simplifying
a = -1x
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 = {-1x, 0.3333333333x}