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Simplifying
(6x + 4y)(6x + -4y) = 0
Multiply (6x + 4y) * (6x + -4y)
(6x * (6x + -4y) + 4y * (6x + -4y)) = 0
((6x * 6x + -4y * 6x) + 4y * (6x + -4y)) = 0
Reorder the terms:
((-24xy + 36x2) + 4y * (6x + -4y)) = 0
((-24xy + 36x2) + 4y * (6x + -4y)) = 0
(-24xy + 36x2 + (6x * 4y + -4y * 4y)) = 0
(-24xy + 36x2 + (24xy + -16y2)) = 0
Reorder the terms:
(-24xy + 24xy + 36x2 + -16y2) = 0
Combine like terms: -24xy + 24xy = 0
(0 + 36x2 + -16y2) = 0
(36x2 + -16y2) = 0
Solving
36x2 + -16y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '16y2' to each side of the equation.
36x2 + -16y2 + 16y2 = 0 + 16y2
Combine like terms: -16y2 + 16y2 = 0
36x2 + 0 = 0 + 16y2
36x2 = 0 + 16y2
Remove the zero:
36x2 = 16y2
Divide each side by '36'.
x2 = 0.4444444444y2
Simplifying
x2 = 0.4444444444y2
Take the square root of each side:
x = {-0.666666667y, 0.666666667y}
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