x^2+5ax-6a^2=0

Solution for x^2+5ax-6a^2=0 equation:

Simplifying
x2 + 5ax + -6a2 = 0

Reorder the terms:
5ax + -6a2 + x2 = 0

Solving
5ax + -6a2 + x2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-6a + -1x)(a + -1x) = 0

Subproblem 1
Set the factor '(-6a + -1x)' equal to zero and attempt to solve:

Simplifying
-6a + -1x = 0

Solving
-6a + -1x = 0

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

Add 'x' to each side of the equation.
-6a + -1x + x = 0 + x

Combine like terms: -1x + x = 0
-6a + 0 = 0 + x
-6a = 0 + x
Remove the zero:
-6a = x

Divide each side by '-6'.
a = -0.1666666667x

Simplifying
a = -0.1666666667x
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 = {-0.1666666667x, x}