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Simplifying
(6x + 9y)(6x + -9y) = 0
Multiply (6x + 9y) * (6x + -9y)
(6x * (6x + -9y) + 9y * (6x + -9y)) = 0
((6x * 6x + -9y * 6x) + 9y * (6x + -9y)) = 0
Reorder the terms:
((-54xy + 36x2) + 9y * (6x + -9y)) = 0
((-54xy + 36x2) + 9y * (6x + -9y)) = 0
(-54xy + 36x2 + (6x * 9y + -9y * 9y)) = 0
(-54xy + 36x2 + (54xy + -81y2)) = 0
Reorder the terms:
(-54xy + 54xy + 36x2 + -81y2) = 0
Combine like terms: -54xy + 54xy = 0
(0 + 36x2 + -81y2) = 0
(36x2 + -81y2) = 0
Solving
36x2 + -81y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '81y2' to each side of the equation.
36x2 + -81y2 + 81y2 = 0 + 81y2
Combine like terms: -81y2 + 81y2 = 0
36x2 + 0 = 0 + 81y2
36x2 = 0 + 81y2
Remove the zero:
36x2 = 81y2
Divide each side by '36'.
x2 = 2.25y2
Simplifying
x2 = 2.25y2
Take the square root of each side:
x = {-1.5y, 1.5y}
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