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Simplifying
(6c + -8d)(6c + 8d) = 0
Multiply (6c + -8d) * (6c + 8d)
(6c * (6c + 8d) + -8d * (6c + 8d)) = 0
((6c * 6c + 8d * 6c) + -8d * (6c + 8d)) = 0
Reorder the terms:
((48cd + 36c2) + -8d * (6c + 8d)) = 0
((48cd + 36c2) + -8d * (6c + 8d)) = 0
(48cd + 36c2 + (6c * -8d + 8d * -8d)) = 0
(48cd + 36c2 + (-48cd + -64d2)) = 0
Reorder the terms:
(48cd + -48cd + 36c2 + -64d2) = 0
Combine like terms: 48cd + -48cd = 0
(0 + 36c2 + -64d2) = 0
(36c2 + -64d2) = 0
Solving
36c2 + -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.
36c2 + -64d2 + 64d2 = 0 + 64d2
Combine like terms: -64d2 + 64d2 = 0
36c2 + 0 = 0 + 64d2
36c2 = 0 + 64d2
Remove the zero:
36c2 = 64d2
Divide each side by '36'.
c2 = 1.777777778d2
Simplifying
c2 = 1.777777778d2
Take the square root of each side:
c = {-1.333333333d, 1.333333333d}
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