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Simplifying
(2x + 1y)(4x + -2y) = 0
Multiply (2x + 1y) * (4x + -2y)
(2x * (4x + -2y) + 1y * (4x + -2y)) = 0
((4x * 2x + -2y * 2x) + 1y * (4x + -2y)) = 0
Reorder the terms:
((-4xy + 8x2) + 1y * (4x + -2y)) = 0
((-4xy + 8x2) + 1y * (4x + -2y)) = 0
(-4xy + 8x2 + (4x * 1y + -2y * 1y)) = 0
(-4xy + 8x2 + (4xy + -2y2)) = 0
Reorder the terms:
(-4xy + 4xy + 8x2 + -2y2) = 0
Combine like terms: -4xy + 4xy = 0
(0 + 8x2 + -2y2) = 0
(8x2 + -2y2) = 0
Solving
8x2 + -2y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '2y2' to each side of the equation.
8x2 + -2y2 + 2y2 = 0 + 2y2
Combine like terms: -2y2 + 2y2 = 0
8x2 + 0 = 0 + 2y2
8x2 = 0 + 2y2
Remove the zero:
8x2 = 2y2
Divide each side by '8'.
x2 = 0.25y2
Simplifying
x2 = 0.25y2
Take the square root of each side:
x = {-0.5y, 0.5y}
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