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Simplifying
(4c + -8d)(4c + 8d) = 0
Multiply (4c + -8d) * (4c + 8d)
(4c * (4c + 8d) + -8d * (4c + 8d)) = 0
((4c * 4c + 8d * 4c) + -8d * (4c + 8d)) = 0
Reorder the terms:
((32cd + 16c2) + -8d * (4c + 8d)) = 0
((32cd + 16c2) + -8d * (4c + 8d)) = 0
(32cd + 16c2 + (4c * -8d + 8d * -8d)) = 0
(32cd + 16c2 + (-32cd + -64d2)) = 0
Reorder the terms:
(32cd + -32cd + 16c2 + -64d2) = 0
Combine like terms: 32cd + -32cd = 0
(0 + 16c2 + -64d2) = 0
(16c2 + -64d2) = 0
Solving
16c2 + -64d2 = 0
Solving for variable 'c'.
Move all terms containing c to the left, all other terms to the right.
Add '64d2' to each side of the equation.
16c2 + -64d2 + 64d2 = 0 + 64d2
Combine like terms: -64d2 + 64d2 = 0
16c2 + 0 = 0 + 64d2
16c2 = 0 + 64d2
Remove the zero:
16c2 = 64d2
Divide each side by '16'.
c2 = 4d2
Simplifying
c2 = 4d2
Take the square root of each side:
c = {-2d, 2d}
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