40x^2+5xy-45y^2=0

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Solution for 40x^2+5xy-45y^2=0 equation:


Simplifying
40x2 + 5xy + -45y2 = 0

Reorder the terms:
5xy + 40x2 + -45y2 = 0

Solving
5xy + 40x2 + -45y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(xy + 8x2 + -9y2) = 0

Factor a trinomial.
5((x + -1y)(8x + 9y)) = 0

Ignore the factor 5.

Subproblem 1

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

Subproblem 2

Set the factor '(8x + 9y)' equal to zero and attempt to solve: Simplifying 8x + 9y = 0 Solving 8x + 9y = 0 Move all terms containing x to the left, all other terms to the right. Add '-9y' to each side of the equation. 8x + 9y + -9y = 0 + -9y Combine like terms: 9y + -9y = 0 8x + 0 = 0 + -9y 8x = 0 + -9y Remove the zero: 8x = -9y Divide each side by '8'. x = -1.125y Simplifying x = -1.125y

Solution

x = {y, -1.125y}

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