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Simplifying
(9x + 6y)(9x + -6y) = 0
Multiply (9x + 6y) * (9x + -6y)
(9x * (9x + -6y) + 6y * (9x + -6y)) = 0
((9x * 9x + -6y * 9x) + 6y * (9x + -6y)) = 0
Reorder the terms:
((-54xy + 81x2) + 6y * (9x + -6y)) = 0
((-54xy + 81x2) + 6y * (9x + -6y)) = 0
(-54xy + 81x2 + (9x * 6y + -6y * 6y)) = 0
(-54xy + 81x2 + (54xy + -36y2)) = 0
Reorder the terms:
(-54xy + 54xy + 81x2 + -36y2) = 0
Combine like terms: -54xy + 54xy = 0
(0 + 81x2 + -36y2) = 0
(81x2 + -36y2) = 0
Solving
81x2 + -36y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '36y2' to each side of the equation.
81x2 + -36y2 + 36y2 = 0 + 36y2
Combine like terms: -36y2 + 36y2 = 0
81x2 + 0 = 0 + 36y2
81x2 = 0 + 36y2
Remove the zero:
81x2 = 36y2
Divide each side by '81'.
x2 = 0.4444444444y2
Simplifying
x2 = 0.4444444444y2
Take the square root of each side:
x = {-0.666666667y, 0.666666667y}
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