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Simplifying
(5x + 3y)(3y + -5x) = 0
Reorder the terms:
(5x + 3y)(-5x + 3y) = 0
Multiply (5x + 3y) * (-5x + 3y)
(5x * (-5x + 3y) + 3y * (-5x + 3y)) = 0
((-5x * 5x + 3y * 5x) + 3y * (-5x + 3y)) = 0
Reorder the terms:
((15xy + -25x2) + 3y * (-5x + 3y)) = 0
((15xy + -25x2) + 3y * (-5x + 3y)) = 0
(15xy + -25x2 + (-5x * 3y + 3y * 3y)) = 0
(15xy + -25x2 + (-15xy + 9y2)) = 0
Reorder the terms:
(15xy + -15xy + -25x2 + 9y2) = 0
Combine like terms: 15xy + -15xy = 0
(0 + -25x2 + 9y2) = 0
(-25x2 + 9y2) = 0
Solving
-25x2 + 9y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-9y2' to each side of the equation.
-25x2 + 9y2 + -9y2 = 0 + -9y2
Combine like terms: 9y2 + -9y2 = 0
-25x2 + 0 = 0 + -9y2
-25x2 = 0 + -9y2
Remove the zero:
-25x2 = -9y2
Divide each side by '-25'.
x2 = 0.36y2
Simplifying
x2 = 0.36y2
Take the square root of each side:
x = {-0.6y, 0.6y}
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