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Simplifying (5c + -3)(6c + -5) = 0 Reorder the terms: (-3 + 5c)(6c + -5) = 0 Reorder the terms: (-3 + 5c)(-5 + 6c) = 0 Multiply (-3 + 5c) * (-5 + 6c) (-3(-5 + 6c) + 5c * (-5 + 6c)) = 0 ((-5 * -3 + 6c * -3) + 5c * (-5 + 6c)) = 0 ((15 + -18c) + 5c * (-5 + 6c)) = 0 (15 + -18c + (-5 * 5c + 6c * 5c)) = 0 (15 + -18c + (-25c + 30c2)) = 0 Combine like terms: -18c + -25c = -43c (15 + -43c + 30c2) = 0 Solving 15 + -43c + 30c2 = 0 Solving for variable 'c'. Factor a trinomial. (3 + -5c)(5 + -6c) = 0Subproblem 1
Set the factor '(3 + -5c)' equal to zero and attempt to solve: Simplifying 3 + -5c = 0 Solving 3 + -5c = 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 + -5c = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5c = 0 + -3 -5c = 0 + -3 Combine like terms: 0 + -3 = -3 -5c = -3 Divide each side by '-5'. c = 0.6 Simplifying c = 0.6Subproblem 2
Set the factor '(5 + -6c)' equal to zero and attempt to solve: Simplifying 5 + -6c = 0 Solving 5 + -6c = 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 + -6c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6c = 0 + -5 -6c = 0 + -5 Combine like terms: 0 + -5 = -5 -6c = -5 Divide each side by '-6'. c = 0.8333333333 Simplifying c = 0.8333333333Solution
c = {0.6, 0.8333333333}
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