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Simplifying (5c + -9d)(5c + 9d) = 0 Multiply (5c + -9d) * (5c + 9d) (5c * (5c + 9d) + -9d * (5c + 9d)) = 0 ((5c * 5c + 9d * 5c) + -9d * (5c + 9d)) = 0 Reorder the terms: ((45cd + 25c2) + -9d * (5c + 9d)) = 0 ((45cd + 25c2) + -9d * (5c + 9d)) = 0 (45cd + 25c2 + (5c * -9d + 9d * -9d)) = 0 (45cd + 25c2 + (-45cd + -81d2)) = 0 Reorder the terms: (45cd + -45cd + 25c2 + -81d2) = 0 Combine like terms: 45cd + -45cd = 0 (0 + 25c2 + -81d2) = 0 (25c2 + -81d2) = 0 Solving 25c2 + -81d2 = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '81d2' to each side of the equation. 25c2 + -81d2 + 81d2 = 0 + 81d2 Combine like terms: -81d2 + 81d2 = 0 25c2 + 0 = 0 + 81d2 25c2 = 0 + 81d2 Remove the zero: 25c2 = 81d2 Divide each side by '25'. c2 = 3.24d2 Simplifying c2 = 3.24d2 Take the square root of each side: c = {-1.8d, 1.8d}
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