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Simplifying
(3x + 2y)(6x + -4y) = 0
Multiply (3x + 2y) * (6x + -4y)
(3x * (6x + -4y) + 2y * (6x + -4y)) = 0
((6x * 3x + -4y * 3x) + 2y * (6x + -4y)) = 0
Reorder the terms:
((-12xy + 18x2) + 2y * (6x + -4y)) = 0
((-12xy + 18x2) + 2y * (6x + -4y)) = 0
(-12xy + 18x2 + (6x * 2y + -4y * 2y)) = 0
(-12xy + 18x2 + (12xy + -8y2)) = 0
Reorder the terms:
(-12xy + 12xy + 18x2 + -8y2) = 0
Combine like terms: -12xy + 12xy = 0
(0 + 18x2 + -8y2) = 0
(18x2 + -8y2) = 0
Solving
18x2 + -8y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '8y2' to each side of the equation.
18x2 + -8y2 + 8y2 = 0 + 8y2
Combine like terms: -8y2 + 8y2 = 0
18x2 + 0 = 0 + 8y2
18x2 = 0 + 8y2
Remove the zero:
18x2 = 8y2
Divide each side by '18'.
x2 = 0.4444444444y2
Simplifying
x2 = 0.4444444444y2
Take the square root of each side:
x = {-0.666666667y, 0.666666667y}
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