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Simplifying (4c + -3d)(7c + -3d) = 0 Multiply (4c + -3d) * (7c + -3d) (4c * (7c + -3d) + -3d * (7c + -3d)) = 0 ((7c * 4c + -3d * 4c) + -3d * (7c + -3d)) = 0 Reorder the terms: ((-12cd + 28c2) + -3d * (7c + -3d)) = 0 ((-12cd + 28c2) + -3d * (7c + -3d)) = 0 (-12cd + 28c2 + (7c * -3d + -3d * -3d)) = 0 (-12cd + 28c2 + (-21cd + 9d2)) = 0 Reorder the terms: (-12cd + -21cd + 28c2 + 9d2) = 0 Combine like terms: -12cd + -21cd = -33cd (-33cd + 28c2 + 9d2) = 0 Solving -33cd + 28c2 + 9d2 = 0 Solving for variable 'c'. Factor a trinomial. (4c + -3d)(7c + -3d) = 0Subproblem 1
Set the factor '(4c + -3d)' equal to zero and attempt to solve: Simplifying 4c + -3d = 0 Solving 4c + -3d = 0 Move all terms containing c to the left, all other terms to the right. Add '3d' to each side of the equation. 4c + -3d + 3d = 0 + 3d Combine like terms: -3d + 3d = 0 4c + 0 = 0 + 3d 4c = 0 + 3d Remove the zero: 4c = 3d Divide each side by '4'. c = 0.75d Simplifying c = 0.75dSubproblem 2
Set the factor '(7c + -3d)' equal to zero and attempt to solve: Simplifying 7c + -3d = 0 Solving 7c + -3d = 0 Move all terms containing c to the left, all other terms to the right. Add '3d' to each side of the equation. 7c + -3d + 3d = 0 + 3d Combine like terms: -3d + 3d = 0 7c + 0 = 0 + 3d 7c = 0 + 3d Remove the zero: 7c = 3d Divide each side by '7'. c = 0.4285714286d Simplifying c = 0.4285714286dSolution
c = {0.75d, 0.4285714286d}
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