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Simplifying 75c2 + 90cd + 27d2 = 0 Reorder the terms: 90cd + 75c2 + 27d2 = 0 Solving 90cd + 75c2 + 27d2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '3'. 3(30cd + 25c2 + 9d2) = 0 Factor a trinomial. 3((5c + 3d)(5c + 3d)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5c + 3d)' equal to zero and attempt to solve: Simplifying 5c + 3d = 0 Solving 5c + 3d = 0 Move all terms containing c to the left, all other terms to the right. Add '-3d' to each side of the equation. 5c + 3d + -3d = 0 + -3d Combine like terms: 3d + -3d = 0 5c + 0 = 0 + -3d 5c = 0 + -3d Remove the zero: 5c = -3d Divide each side by '5'. c = -0.6d Simplifying c = -0.6dSubproblem 2
Set the factor '(5c + 3d)' equal to zero and attempt to solve: Simplifying 5c + 3d = 0 Solving 5c + 3d = 0 Move all terms containing c to the left, all other terms to the right. Add '-3d' to each side of the equation. 5c + 3d + -3d = 0 + -3d Combine like terms: 3d + -3d = 0 5c + 0 = 0 + -3d 5c = 0 + -3d Remove the zero: 5c = -3d Divide each side by '5'. c = -0.6d Simplifying c = -0.6dSolution
c = {-0.6d, -0.6d}
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