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Simplifying
(3x + -2y)(3x + 2y) = 0
Multiply (3x + -2y) * (3x + 2y)
(3x * (3x + 2y) + -2y * (3x + 2y)) = 0
((3x * 3x + 2y * 3x) + -2y * (3x + 2y)) = 0
Reorder the terms:
((6xy + 9x2) + -2y * (3x + 2y)) = 0
((6xy + 9x2) + -2y * (3x + 2y)) = 0
(6xy + 9x2 + (3x * -2y + 2y * -2y)) = 0
(6xy + 9x2 + (-6xy + -4y2)) = 0
Reorder the terms:
(6xy + -6xy + 9x2 + -4y2) = 0
Combine like terms: 6xy + -6xy = 0
(0 + 9x2 + -4y2) = 0
(9x2 + -4y2) = 0
Solving
9x2 + -4y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '4y2' to each side of the equation.
9x2 + -4y2 + 4y2 = 0 + 4y2
Combine like terms: -4y2 + 4y2 = 0
9x2 + 0 = 0 + 4y2
9x2 = 0 + 4y2
Remove the zero:
9x2 = 4y2
Divide each side by '9'.
x2 = 0.4444444444y2
Simplifying
x2 = 0.4444444444y2
Take the square root of each side:
x = {-0.666666667y, 0.666666667y}
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