20x^2-40xy+15y^2=0

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Solution for 20x^2-40xy+15y^2=0 equation:


Simplifying
20x2 + -40xy + 15y2 = 0

Reorder the terms:
-40xy + 20x2 + 15y2 = 0

Solving
-40xy + 20x2 + 15y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-8xy + 4x2 + 3y2) = 0

Factor a trinomial.
5((2x + -3y)(2x + -1y)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(2x + -3y)' equal to zero and attempt to solve: Simplifying 2x + -3y = 0 Solving 2x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 2x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 2x + 0 = 0 + 3y 2x = 0 + 3y Remove the zero: 2x = 3y Divide each side by '2'. x = 1.5y Simplifying x = 1.5y

Subproblem 2

Set the factor '(2x + -1y)' equal to zero and attempt to solve: Simplifying 2x + -1y = 0 Solving 2x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 2x + -1y + y = 0 + y Combine like terms: -1y + y = 0 2x + 0 = 0 + y 2x = 0 + y Remove the zero: 2x = y Divide each side by '2'. x = 0.5y Simplifying x = 0.5y

Solution

x = {1.5y, 0.5y}

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