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

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

Simplifying
2x2 + ax + -1a2 = 0

Reorder the terms:
ax + -1a2 + 2x2 = 0

Solving
ax + -1a2 + 2x2 = 0

Solving for variable 'a'.

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

Simplifying
a + -2x = 0

Solving
a + -2x = 0

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

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

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

Simplifying
a = 2x
Solution
a = {-1x, 2x}