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Simplifying (3c + -1d)(2c + -7d) = 0 Multiply (3c + -1d) * (2c + -7d) (3c * (2c + -7d) + -1d * (2c + -7d)) = 0 ((2c * 3c + -7d * 3c) + -1d * (2c + -7d)) = 0 Reorder the terms: ((-21cd + 6c2) + -1d * (2c + -7d)) = 0 ((-21cd + 6c2) + -1d * (2c + -7d)) = 0 (-21cd + 6c2 + (2c * -1d + -7d * -1d)) = 0 (-21cd + 6c2 + (-2cd + 7d2)) = 0 Reorder the terms: (-21cd + -2cd + 6c2 + 7d2) = 0 Combine like terms: -21cd + -2cd = -23cd (-23cd + 6c2 + 7d2) = 0 Solving -23cd + 6c2 + 7d2 = 0 Solving for variable 'c'. Factor a trinomial. (2c + -7d)(3c + -1d) = 0Subproblem 1
Set the factor '(2c + -7d)' equal to zero and attempt to solve: Simplifying 2c + -7d = 0 Solving 2c + -7d = 0 Move all terms containing c to the left, all other terms to the right. Add '7d' to each side of the equation. 2c + -7d + 7d = 0 + 7d Combine like terms: -7d + 7d = 0 2c + 0 = 0 + 7d 2c = 0 + 7d Remove the zero: 2c = 7d Divide each side by '2'. c = 3.5d Simplifying c = 3.5dSubproblem 2
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 = 0.3333333333dSolution
c = {3.5d, 0.3333333333d}
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