3x^2+2ax-5a^2=0

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Solution for 3x^2+2ax-5a^2=0 equation: 


Simplifying
3x2 + 2ax + -5a2 = 0

Reorder the terms:
2ax + -5a2 + 3x2 = 0

Solving
2ax + -5a2 + 3x2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5a + -3x)(a + -1x) = 0


Subproblem 1
Set the factor '(-5a + -3x)' equal to zero and attempt to solve:

Simplifying
-5a + -3x = 0

Solving
-5a + -3x = 0

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

Add '3x' to each side of the equation.
-5a + -3x + 3x = 0 + 3x

Combine like terms: -3x + 3x = 0
-5a + 0 = 0 + 3x
-5a = 0 + 3x
Remove the zero:
-5a = 3x

Divide each side by '-5'.
a = -0.6x

Simplifying
a = -0.6x

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 = {-0.6x, x}

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