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Simplifying
(3x + -1y)(3x + y) = 0
Multiply (3x + -1y) * (3x + y)
(3x * (3x + y) + -1y * (3x + y)) = 0
((3x * 3x + y * 3x) + -1y * (3x + y)) = 0
Reorder the terms:
((3xy + 9x2) + -1y * (3x + y)) = 0
((3xy + 9x2) + -1y * (3x + y)) = 0
(3xy + 9x2 + (3x * -1y + y * -1y)) = 0
(3xy + 9x2 + (-3xy + -1y2)) = 0
Reorder the terms:
(3xy + -3xy + 9x2 + -1y2) = 0
Combine like terms: 3xy + -3xy = 0
(0 + 9x2 + -1y2) = 0
(9x2 + -1y2) = 0
Solving
9x2 + -1y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add 'y2' to each side of the equation.
9x2 + -1y2 + y2 = 0 + y2
Combine like terms: -1y2 + y2 = 0
9x2 + 0 = 0 + y2
9x2 = 0 + y2
Remove the zero:
9x2 = y2
Divide each side by '9'.
x2 = 0.1111111111y2
Simplifying
x2 = 0.1111111111y2
Take the square root of each side:
x = {-0.333333333y, 0.333333333y}
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