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Simplifying (3c + 4)(5 + 2c) = 0 Reorder the terms: (4 + 3c)(5 + 2c) = 0 Multiply (4 + 3c) * (5 + 2c) (4(5 + 2c) + 3c * (5 + 2c)) = 0 ((5 * 4 + 2c * 4) + 3c * (5 + 2c)) = 0 ((20 + 8c) + 3c * (5 + 2c)) = 0 (20 + 8c + (5 * 3c + 2c * 3c)) = 0 (20 + 8c + (15c + 6c2)) = 0 Combine like terms: 8c + 15c = 23c (20 + 23c + 6c2) = 0 Solving 20 + 23c + 6c2 = 0 Solving for variable 'c'. Factor a trinomial. (5 + 2c)(4 + 3c) = 0Subproblem 1
Set the factor '(5 + 2c)' equal to zero and attempt to solve: Simplifying 5 + 2c = 0 Solving 5 + 2c = 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 + 2c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2c = 0 + -5 2c = 0 + -5 Combine like terms: 0 + -5 = -5 2c = -5 Divide each side by '2'. c = -2.5 Simplifying c = -2.5Subproblem 2
Set the factor '(4 + 3c)' equal to zero and attempt to solve: Simplifying 4 + 3c = 0 Solving 4 + 3c = 0 Move all terms containing c to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3c = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3c = 0 + -4 3c = 0 + -4 Combine like terms: 0 + -4 = -4 3c = -4 Divide each side by '3'. c = -1.333333333 Simplifying c = -1.333333333Solution
c = {-2.5, -1.333333333}
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