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Simplifying (c + 1)(3c + 2) = 44 Reorder the terms: (1 + c)(3c + 2) = 44 Reorder the terms: (1 + c)(2 + 3c) = 44 Multiply (1 + c) * (2 + 3c) (1(2 + 3c) + c(2 + 3c)) = 44 ((2 * 1 + 3c * 1) + c(2 + 3c)) = 44 ((2 + 3c) + c(2 + 3c)) = 44 (2 + 3c + (2 * c + 3c * c)) = 44 (2 + 3c + (2c + 3c2)) = 44 Combine like terms: 3c + 2c = 5c (2 + 5c + 3c2) = 44 Solving 2 + 5c + 3c2 = 44 Solving for variable 'c'. Reorder the terms: 2 + -44 + 5c + 3c2 = 44 + -44 Combine like terms: 2 + -44 = -42 -42 + 5c + 3c2 = 44 + -44 Combine like terms: 44 + -44 = 0 -42 + 5c + 3c2 = 0 Factor a trinomial. (-14 + -3c)(3 + -1c) = 0Subproblem 1
Set the factor '(-14 + -3c)' equal to zero and attempt to solve: Simplifying -14 + -3c = 0 Solving -14 + -3c = 0 Move all terms containing c to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + -3c = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -3c = 0 + 14 -3c = 0 + 14 Combine like terms: 0 + 14 = 14 -3c = 14 Divide each side by '-3'. c = -4.666666667 Simplifying c = -4.666666667Subproblem 2
Set the factor '(3 + -1c)' equal to zero and attempt to solve: Simplifying 3 + -1c = 0 Solving 3 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1c = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1c = 0 + -3 -1c = 0 + -3 Combine like terms: 0 + -3 = -3 -1c = -3 Divide each side by '-1'. c = 3 Simplifying c = 3Solution
c = {-4.666666667, 3}
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