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Simplifying (3c + -1d)(7c + 4d) = 0 Multiply (3c + -1d) * (7c + 4d) (3c * (7c + 4d) + -1d * (7c + 4d)) = 0 ((7c * 3c + 4d * 3c) + -1d * (7c + 4d)) = 0 Reorder the terms: ((12cd + 21c2) + -1d * (7c + 4d)) = 0 ((12cd + 21c2) + -1d * (7c + 4d)) = 0 (12cd + 21c2 + (7c * -1d + 4d * -1d)) = 0 (12cd + 21c2 + (-7cd + -4d2)) = 0 Reorder the terms: (12cd + -7cd + 21c2 + -4d2) = 0 Combine like terms: 12cd + -7cd = 5cd (5cd + 21c2 + -4d2) = 0 Solving 5cd + 21c2 + -4d2 = 0 Solving for variable 'c'. Factor a trinomial. (3c + -1d)(7c + 4d) = 0Subproblem 1
Set the factor '(3c + -1d)' equal to zero and attempt to solve: Simplifying 3c + -1d = 0 Solving 3c + -1d = 0 Move all terms containing c to the left, all other terms to the right. Add 'd' to each side of the equation. 3c + -1d + d = 0 + d Combine like terms: -1d + d = 0 3c + 0 = 0 + d 3c = 0 + d Remove the zero: 3c = d Divide each side by '3'. c = 0.3333333333d Simplifying c = 0.3333333333dSubproblem 2
Set the factor '(7c + 4d)' equal to zero and attempt to solve: Simplifying 7c + 4d = 0 Solving 7c + 4d = 0 Move all terms containing c to the left, all other terms to the right. Add '-4d' to each side of the equation. 7c + 4d + -4d = 0 + -4d Combine like terms: 4d + -4d = 0 7c + 0 = 0 + -4d 7c = 0 + -4d Remove the zero: 7c = -4d Divide each side by '7'. c = -0.5714285714d Simplifying c = -0.5714285714dSolution
c = {0.3333333333d, -0.5714285714d}
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