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Simplifying (5c + 7d)(c + d) = 0 Multiply (5c + 7d) * (c + d) (5c * (c + d) + 7d * (c + d)) = 0 ((c * 5c + d * 5c) + 7d * (c + d)) = 0 Reorder the terms: ((5cd + 5c2) + 7d * (c + d)) = 0 ((5cd + 5c2) + 7d * (c + d)) = 0 (5cd + 5c2 + (c * 7d + d * 7d)) = 0 (5cd + 5c2 + (7cd + 7d2)) = 0 Reorder the terms: (5cd + 7cd + 5c2 + 7d2) = 0 Combine like terms: 5cd + 7cd = 12cd (12cd + 5c2 + 7d2) = 0 Solving 12cd + 5c2 + 7d2 = 0 Solving for variable 'c'. Factor a trinomial. (c + d)(5c + 7d) = 0Subproblem 1
Set the factor '(c + d)' equal to zero and attempt to solve: Simplifying c + d = 0 Solving c + d = 0 Move all terms containing c to the left, all other terms to the right. Add '-1d' to each side of the equation. c + d + -1d = 0 + -1d Combine like terms: d + -1d = 0 c + 0 = 0 + -1d c = 0 + -1d Remove the zero: c = -1d Simplifying c = -1dSubproblem 2
Set the factor '(5c + 7d)' equal to zero and attempt to solve: Simplifying 5c + 7d = 0 Solving 5c + 7d = 0 Move all terms containing c to the left, all other terms to the right. Add '-7d' to each side of the equation. 5c + 7d + -7d = 0 + -7d Combine like terms: 7d + -7d = 0 5c + 0 = 0 + -7d 5c = 0 + -7d Remove the zero: 5c = -7d Divide each side by '5'. c = -1.4d Simplifying c = -1.4dSolution
c = {-1d, -1.4d}
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