40x^2-7xy-20y^2=0

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Solution for 40x^2-7xy-20y^2=0 equation: 


Simplifying
40x2 + -7xy + -20y2 = 0

Reorder the terms:
-7xy + 40x2 + -20y2 = 0

Solving
-7xy + 40x2 + -20y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + -4y)(8x + 5y) = 0


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

Simplifying
5x + -4y = 0

Solving
5x + -4y = 0

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

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

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

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

Simplifying
x = 0.8y

Subproblem 2
Set the factor '(8x + 5y)' equal to zero and attempt to solve:

Simplifying
8x + 5y = 0

Solving
8x + 5y = 0

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

Add '-5y' to each side of the equation.
8x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
8x + 0 = 0 + -5y
8x = 0 + -5y
Remove the zero:
8x = -5y

Divide each side by '8'.
x = -0.625y

Simplifying
x = -0.625y
Solution
x = {0.8y, -0.625y}

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