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Simplifying 12c2 + 36cd + 27d2 = 0 Reorder the terms: 36cd + 12c2 + 27d2 = 0 Solving 36cd + 12c2 + 27d2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '3'. 3(12cd + 4c2 + 9d2) = 0 Factor a trinomial. 3((2c + 3d)(2c + 3d)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2c + 3d)' equal to zero and attempt to solve: Simplifying 2c + 3d = 0 Solving 2c + 3d = 0 Move all terms containing c to the left, all other terms to the right. Add '-3d' to each side of the equation. 2c + 3d + -3d = 0 + -3d Combine like terms: 3d + -3d = 0 2c + 0 = 0 + -3d 2c = 0 + -3d Remove the zero: 2c = -3d Divide each side by '2'. c = -1.5d Simplifying c = -1.5dSubproblem 2
Set the factor '(2c + 3d)' equal to zero and attempt to solve: Simplifying 2c + 3d = 0 Solving 2c + 3d = 0 Move all terms containing c to the left, all other terms to the right. Add '-3d' to each side of the equation. 2c + 3d + -3d = 0 + -3d Combine like terms: 3d + -3d = 0 2c + 0 = 0 + -3d 2c = 0 + -3d Remove the zero: 2c = -3d Divide each side by '2'. c = -1.5d Simplifying c = -1.5dSolution
c = {-1.5d, -1.5d}
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