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Simplifying (2c + -1d)(3c + d) = 0 Multiply (2c + -1d) * (3c + d) (2c * (3c + d) + -1d * (3c + d)) = 0 ((3c * 2c + d * 2c) + -1d * (3c + d)) = 0 Reorder the terms: ((2cd + 6c2) + -1d * (3c + d)) = 0 ((2cd + 6c2) + -1d * (3c + d)) = 0 (2cd + 6c2 + (3c * -1d + d * -1d)) = 0 (2cd + 6c2 + (-3cd + -1d2)) = 0 Reorder the terms: (2cd + -3cd + 6c2 + -1d2) = 0 Combine like terms: 2cd + -3cd = -1cd (-1cd + 6c2 + -1d2) = 0 Solving -1cd + 6c2 + -1d2 = 0 Solving for variable 'c'. Factor a trinomial. (2c + -1d)(3c + d) = 0Subproblem 1
Set the factor '(2c + -1d)' equal to zero and attempt to solve: Simplifying 2c + -1d = 0 Solving 2c + -1d = 0 Move all terms containing c to the left, all other terms to the right. Add 'd' to each side of the equation. 2c + -1d + d = 0 + d Combine like terms: -1d + d = 0 2c + 0 = 0 + d 2c = 0 + d Remove the zero: 2c = d Divide each side by '2'. c = 0.5d Simplifying c = 0.5dSubproblem 2
Set the factor '(3c + d)' equal to zero and attempt to solve: Simplifying 3c + d = 0 Solving 3c + d = 0 Move all terms containing c to the left, all other terms to the right. Add '-1d' to each side of the equation. 3c + d + -1d = 0 + -1d Combine like terms: d + -1d = 0 3c + 0 = 0 + -1d 3c = 0 + -1d Remove the zero: 3c = -1d Divide each side by '3'. c = -0.3333333333d Simplifying c = -0.3333333333dSolution
c = {0.5d, -0.3333333333d}
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