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Simplifying
(6x + 8y)(6x + -8y) = 0
Multiply (6x + 8y) * (6x + -8y)
(6x * (6x + -8y) + 8y * (6x + -8y)) = 0
((6x * 6x + -8y * 6x) + 8y * (6x + -8y)) = 0
Reorder the terms:
((-48xy + 36x2) + 8y * (6x + -8y)) = 0
((-48xy + 36x2) + 8y * (6x + -8y)) = 0
(-48xy + 36x2 + (6x * 8y + -8y * 8y)) = 0
(-48xy + 36x2 + (48xy + -64y2)) = 0
Reorder the terms:
(-48xy + 48xy + 36x2 + -64y2) = 0
Combine like terms: -48xy + 48xy = 0
(0 + 36x2 + -64y2) = 0
(36x2 + -64y2) = 0
Solving
36x2 + -64y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '64y2' to each side of the equation.
36x2 + -64y2 + 64y2 = 0 + 64y2
Combine like terms: -64y2 + 64y2 = 0
36x2 + 0 = 0 + 64y2
36x2 = 0 + 64y2
Remove the zero:
36x2 = 64y2
Divide each side by '36'.
x2 = 1.777777778y2
Simplifying
x2 = 1.777777778y2
Take the square root of each side:
x = {-1.333333333y, 1.333333333y}
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