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Simplifying (4c + 5)(6c + -5) = 0 Reorder the terms: (5 + 4c)(6c + -5) = 0 Reorder the terms: (5 + 4c)(-5 + 6c) = 0 Multiply (5 + 4c) * (-5 + 6c) (5(-5 + 6c) + 4c * (-5 + 6c)) = 0 ((-5 * 5 + 6c * 5) + 4c * (-5 + 6c)) = 0 ((-25 + 30c) + 4c * (-5 + 6c)) = 0 (-25 + 30c + (-5 * 4c + 6c * 4c)) = 0 (-25 + 30c + (-20c + 24c2)) = 0 Combine like terms: 30c + -20c = 10c (-25 + 10c + 24c2) = 0 Solving -25 + 10c + 24c2 = 0 Solving for variable 'c'. Factor a trinomial. (-5 + -4c)(5 + -6c) = 0Subproblem 1
Set the factor '(-5 + -4c)' equal to zero and attempt to solve: Simplifying -5 + -4c = 0 Solving -5 + -4c = 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 + -4c = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4c = 0 + 5 -4c = 0 + 5 Combine like terms: 0 + 5 = 5 -4c = 5 Divide each side by '-4'. c = -1.25 Simplifying c = -1.25Subproblem 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 = {-1.25, 0.8333333333}
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