20x^2-9xa-20a^2=0

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Solution for 20x^2-9xa-20a^2=0 equation: 


Simplifying
20x2 + -9xa + -20a2 = 0

Reorder the terms:
-9ax + -20a2 + 20x2 = 0

Solving
-9ax + -20a2 + 20x2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-4a + -5x)(5a + -4x) = 0


Subproblem 1
Set the factor '(-4a + -5x)' equal to zero and attempt to solve:

Simplifying
-4a + -5x = 0

Solving
-4a + -5x = 0

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

Add '5x' to each side of the equation.
-4a + -5x + 5x = 0 + 5x

Combine like terms: -5x + 5x = 0
-4a + 0 = 0 + 5x
-4a = 0 + 5x
Remove the zero:
-4a = 5x

Divide each side by '-4'.
a = -1.25x

Simplifying
a = -1.25x

Subproblem 2
Set the factor '(5a + -4x)' equal to zero and attempt to solve:

Simplifying
5a + -4x = 0

Solving
5a + -4x = 0

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

Add '4x' to each side of the equation.
5a + -4x + 4x = 0 + 4x

Combine like terms: -4x + 4x = 0
5a + 0 = 0 + 4x
5a = 0 + 4x
Remove the zero:
5a = 4x

Divide each side by '5'.
a = 0.8x

Simplifying
a = 0.8x
Solution
a = {-1.25x, 0.8x}

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