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Simplifying
(3x + -5y)(3x + 5y) = 0
Multiply (3x + -5y) * (3x + 5y)
(3x * (3x + 5y) + -5y * (3x + 5y)) = 0
((3x * 3x + 5y * 3x) + -5y * (3x + 5y)) = 0
Reorder the terms:
((15xy + 9x2) + -5y * (3x + 5y)) = 0
((15xy + 9x2) + -5y * (3x + 5y)) = 0
(15xy + 9x2 + (3x * -5y + 5y * -5y)) = 0
(15xy + 9x2 + (-15xy + -25y2)) = 0
Reorder the terms:
(15xy + -15xy + 9x2 + -25y2) = 0
Combine like terms: 15xy + -15xy = 0
(0 + 9x2 + -25y2) = 0
(9x2 + -25y2) = 0
Solving
9x2 + -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.
9x2 + -25y2 + 25y2 = 0 + 25y2
Combine like terms: -25y2 + 25y2 = 0
9x2 + 0 = 0 + 25y2
9x2 = 0 + 25y2
Remove the zero:
9x2 = 25y2
Divide each side by '9'.
x2 = 2.777777778y2
Simplifying
x2 = 2.777777778y2
Take the square root of each side:
x = {-1.666666667y, 1.666666667y}
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