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Simplifying
(4x + 2y)(4x + -2y) = 0
Multiply (4x + 2y) * (4x + -2y)
(4x * (4x + -2y) + 2y * (4x + -2y)) = 0
((4x * 4x + -2y * 4x) + 2y * (4x + -2y)) = 0
Reorder the terms:
((-8xy + 16x2) + 2y * (4x + -2y)) = 0
((-8xy + 16x2) + 2y * (4x + -2y)) = 0
(-8xy + 16x2 + (4x * 2y + -2y * 2y)) = 0
(-8xy + 16x2 + (8xy + -4y2)) = 0
Reorder the terms:
(-8xy + 8xy + 16x2 + -4y2) = 0
Combine like terms: -8xy + 8xy = 0
(0 + 16x2 + -4y2) = 0
(16x2 + -4y2) = 0
Solving
16x2 + -4y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '4y2' to each side of the equation.
16x2 + -4y2 + 4y2 = 0 + 4y2
Combine like terms: -4y2 + 4y2 = 0
16x2 + 0 = 0 + 4y2
16x2 = 0 + 4y2
Remove the zero:
16x2 = 4y2
Divide each side by '16'.
x2 = 0.25y2
Simplifying
x2 = 0.25y2
Take the square root of each side:
x = {-0.5y, 0.5y}
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