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Simplifying (5c + 7)(c + 5) = 23 Reorder the terms: (7 + 5c)(c + 5) = 23 Reorder the terms: (7 + 5c)(5 + c) = 23 Multiply (7 + 5c) * (5 + c) (7(5 + c) + 5c * (5 + c)) = 23 ((5 * 7 + c * 7) + 5c * (5 + c)) = 23 ((35 + 7c) + 5c * (5 + c)) = 23 (35 + 7c + (5 * 5c + c * 5c)) = 23 (35 + 7c + (25c + 5c2)) = 23 Combine like terms: 7c + 25c = 32c (35 + 32c + 5c2) = 23 Solving 35 + 32c + 5c2 = 23 Solving for variable 'c'. Reorder the terms: 35 + -23 + 32c + 5c2 = 23 + -23 Combine like terms: 35 + -23 = 12 12 + 32c + 5c2 = 23 + -23 Combine like terms: 23 + -23 = 0 12 + 32c + 5c2 = 0 Factor a trinomial. (6 + c)(2 + 5c) = 0Subproblem 1
Set the factor '(6 + c)' equal to zero and attempt to solve: Simplifying 6 + c = 0 Solving 6 + c = 0 Move all terms containing c to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + c = 0 + -6 Combine like terms: 6 + -6 = 0 0 + c = 0 + -6 c = 0 + -6 Combine like terms: 0 + -6 = -6 c = -6 Simplifying c = -6Subproblem 2
Set the factor '(2 + 5c)' equal to zero and attempt to solve: Simplifying 2 + 5c = 0 Solving 2 + 5c = 0 Move all terms containing c to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5c = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5c = 0 + -2 5c = 0 + -2 Combine like terms: 0 + -2 = -2 5c = -2 Divide each side by '5'. c = -0.4 Simplifying c = -0.4Solution
c = {-6, -0.4}
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