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Simplifying (4c + -1d)(c + -5d) = 0 Multiply (4c + -1d) * (c + -5d) (4c * (c + -5d) + -1d * (c + -5d)) = 0 ((c * 4c + -5d * 4c) + -1d * (c + -5d)) = 0 Reorder the terms: ((-20cd + 4c2) + -1d * (c + -5d)) = 0 ((-20cd + 4c2) + -1d * (c + -5d)) = 0 (-20cd + 4c2 + (c * -1d + -5d * -1d)) = 0 (-20cd + 4c2 + (-1cd + 5d2)) = 0 Reorder the terms: (-20cd + -1cd + 4c2 + 5d2) = 0 Combine like terms: -20cd + -1cd = -21cd (-21cd + 4c2 + 5d2) = 0 Solving -21cd + 4c2 + 5d2 = 0 Solving for variable 'c'. Factor a trinomial. (c + -5d)(4c + -1d) = 0Subproblem 1
Set the factor '(c + -5d)' equal to zero and attempt to solve: Simplifying c + -5d = 0 Solving c + -5d = 0 Move all terms containing c to the left, all other terms to the right. Add '5d' to each side of the equation. c + -5d + 5d = 0 + 5d Combine like terms: -5d + 5d = 0 c + 0 = 0 + 5d c = 0 + 5d Remove the zero: c = 5d Simplifying c = 5dSubproblem 2
Set the factor '(4c + -1d)' equal to zero and attempt to solve: Simplifying 4c + -1d = 0 Solving 4c + -1d = 0 Move all terms containing c to the left, all other terms to the right. Add 'd' to each side of the equation. 4c + -1d + d = 0 + d Combine like terms: -1d + d = 0 4c + 0 = 0 + d 4c = 0 + d Remove the zero: 4c = d Divide each side by '4'. c = 0.25d Simplifying c = 0.25dSolution
c = {5d, 0.25d}
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