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Simplifying
(6x + -5y)(5y + 6x) = 0
Reorder the terms:
(6x + -5y)(6x + 5y) = 0
Multiply (6x + -5y) * (6x + 5y)
(6x * (6x + 5y) + -5y * (6x + 5y)) = 0
((6x * 6x + 5y * 6x) + -5y * (6x + 5y)) = 0
Reorder the terms:
((30xy + 36x2) + -5y * (6x + 5y)) = 0
((30xy + 36x2) + -5y * (6x + 5y)) = 0
(30xy + 36x2 + (6x * -5y + 5y * -5y)) = 0
(30xy + 36x2 + (-30xy + -25y2)) = 0
Reorder the terms:
(30xy + -30xy + 36x2 + -25y2) = 0
Combine like terms: 30xy + -30xy = 0
(0 + 36x2 + -25y2) = 0
(36x2 + -25y2) = 0
Solving
36x2 + -25y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '25y2' to each side of the equation.
36x2 + -25y2 + 25y2 = 0 + 25y2
Combine like terms: -25y2 + 25y2 = 0
36x2 + 0 = 0 + 25y2
36x2 = 0 + 25y2
Remove the zero:
36x2 = 25y2
Divide each side by '36'.
x2 = 0.6944444444y2
Simplifying
x2 = 0.6944444444y2
Take the square root of each side:
x = {-0.833333333y, 0.833333333y}
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