(x^2)+ax-(2a^2)=0

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

Simplifying
(x2) + ax + -1(2a2) = 0
x2 + ax + -1(2a2) = 0

Remove parenthesis around (2a2)
x2 + ax + -1 * 2a2 = 0

Multiply -1 * 2
x2 + ax + -2a2 = 0

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

Solving
ax + -2a2 + x2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-2a + -1x)(a + -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 '(a + -1x)' equal to zero and attempt to solve:

Simplifying
a + -1x = 0

Solving
a + -1x = 0

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

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

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

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