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Simplifying c(3d + 4e) + -2c(d + 5e) = 0 (3d * c + 4e * c) + -2c(d + 5e) = 0 (3cd + 4ce) + -2c(d + 5e) = 0 3cd + 4ce + (d * -2c + 5e * -2c) = 0 3cd + 4ce + (-2cd + -10ce) = 0 Reorder the terms: 3cd + -2cd + 4ce + -10ce = 0 Combine like terms: 3cd + -2cd = 1cd 1cd + 4ce + -10ce = 0 Combine like terms: 4ce + -10ce = -6ce 1cd + -6ce = 0 Solving 1cd + -6ce = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'c'. c(d + -6e) = 0Subproblem 1
Set the factor 'c' equal to zero and attempt to solve: Simplifying c = 0 Solving c = 0 Move all terms containing c to the left, all other terms to the right. Simplifying c = 0Subproblem 2
Set the factor '(d + -6e)' equal to zero and attempt to solve: Simplifying d + -6e = 0 Solving d + -6e = 0 Move all terms containing c to the left, all other terms to the right. Add '-1d' to each side of the equation. d + -1d + -6e = 0 + -1d Combine like terms: d + -1d = 0 0 + -6e = 0 + -1d -6e = 0 + -1d Remove the zero: -6e = -1d Add '6e' to each side of the equation. -6e + 6e = -1d + 6e Combine like terms: -6e + 6e = 0 0 = -1d + 6e Simplifying 0 = -1d + 6e The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
c = {0}
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