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Simplifying
(6c + -6d)(5c + 5d) = 0
Multiply (6c + -6d) * (5c + 5d)
(6c * (5c + 5d) + -6d * (5c + 5d)) = 0
((5c * 6c + 5d * 6c) + -6d * (5c + 5d)) = 0
Reorder the terms:
((30cd + 30c2) + -6d * (5c + 5d)) = 0
((30cd + 30c2) + -6d * (5c + 5d)) = 0
(30cd + 30c2 + (5c * -6d + 5d * -6d)) = 0
(30cd + 30c2 + (-30cd + -30d2)) = 0
Reorder the terms:
(30cd + -30cd + 30c2 + -30d2) = 0
Combine like terms: 30cd + -30cd = 0
(0 + 30c2 + -30d2) = 0
(30c2 + -30d2) = 0
Solving
30c2 + -30d2 = 0
Solving for variable 'c'.
Move all terms containing c to the left, all other terms to the right.
Add '30d2' to each side of the equation.
30c2 + -30d2 + 30d2 = 0 + 30d2
Combine like terms: -30d2 + 30d2 = 0
30c2 + 0 = 0 + 30d2
30c2 = 0 + 30d2
Remove the zero:
30c2 = 30d2
Divide each side by '30'.
c2 = d2
Simplifying
c2 = d2
Take the square root of each side:
c = {-1d, d}
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