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Simplifying
(4x + 8y)(4x + -8y) = 0
Multiply (4x + 8y) * (4x + -8y)
(4x * (4x + -8y) + 8y * (4x + -8y)) = 0
((4x * 4x + -8y * 4x) + 8y * (4x + -8y)) = 0
Reorder the terms:
((-32xy + 16x2) + 8y * (4x + -8y)) = 0
((-32xy + 16x2) + 8y * (4x + -8y)) = 0
(-32xy + 16x2 + (4x * 8y + -8y * 8y)) = 0
(-32xy + 16x2 + (32xy + -64y2)) = 0
Reorder the terms:
(-32xy + 32xy + 16x2 + -64y2) = 0
Combine like terms: -32xy + 32xy = 0
(0 + 16x2 + -64y2) = 0
(16x2 + -64y2) = 0
Solving
16x2 + -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.
16x2 + -64y2 + 64y2 = 0 + 64y2
Combine like terms: -64y2 + 64y2 = 0
16x2 + 0 = 0 + 64y2
16x2 = 0 + 64y2
Remove the zero:
16x2 = 64y2
Divide each side by '16'.
x2 = 4y2
Simplifying
x2 = 4y2
Take the square root of each side:
x = {-2y, 2y}
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