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Simplifying (3c + 5)(5c + 7) = 0 Reorder the terms: (5 + 3c)(5c + 7) = 0 Reorder the terms: (5 + 3c)(7 + 5c) = 0 Multiply (5 + 3c) * (7 + 5c) (5(7 + 5c) + 3c * (7 + 5c)) = 0 ((7 * 5 + 5c * 5) + 3c * (7 + 5c)) = 0 ((35 + 25c) + 3c * (7 + 5c)) = 0 (35 + 25c + (7 * 3c + 5c * 3c)) = 0 (35 + 25c + (21c + 15c2)) = 0 Combine like terms: 25c + 21c = 46c (35 + 46c + 15c2) = 0 Solving 35 + 46c + 15c2 = 0 Solving for variable 'c'. Factor a trinomial. (5 + 3c)(7 + 5c) = 0Subproblem 1
Set the factor '(5 + 3c)' equal to zero and attempt to solve: Simplifying 5 + 3c = 0 Solving 5 + 3c = 0 Move all terms containing c to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3c = 0 + -5 3c = 0 + -5 Combine like terms: 0 + -5 = -5 3c = -5 Divide each side by '3'. c = -1.666666667 Simplifying c = -1.666666667Subproblem 2
Set the factor '(7 + 5c)' equal to zero and attempt to solve: Simplifying 7 + 5c = 0 Solving 7 + 5c = 0 Move all terms containing c to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 5c = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5c = 0 + -7 5c = 0 + -7 Combine like terms: 0 + -7 = -7 5c = -7 Divide each side by '5'. c = -1.4 Simplifying c = -1.4Solution
c = {-1.666666667, -1.4}
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