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Simplifying (5c + -4f)(5c + 3f) = 0 Multiply (5c + -4f) * (5c + 3f) (5c * (5c + 3f) + -4f * (5c + 3f)) = 0 ((5c * 5c + 3f * 5c) + -4f * (5c + 3f)) = 0 Reorder the terms: ((15cf + 25c2) + -4f * (5c + 3f)) = 0 ((15cf + 25c2) + -4f * (5c + 3f)) = 0 (15cf + 25c2 + (5c * -4f + 3f * -4f)) = 0 (15cf + 25c2 + (-20cf + -12f2)) = 0 Reorder the terms: (15cf + -20cf + 25c2 + -12f2) = 0 Combine like terms: 15cf + -20cf = -5cf (-5cf + 25c2 + -12f2) = 0 Solving -5cf + 25c2 + -12f2 = 0 Solving for variable 'c'. Factor a trinomial. (5c + -4f)(5c + 3f) = 0Subproblem 1
Set the factor '(5c + -4f)' equal to zero and attempt to solve: Simplifying 5c + -4f = 0 Solving 5c + -4f = 0 Move all terms containing c to the left, all other terms to the right. Add '4f' to each side of the equation. 5c + -4f + 4f = 0 + 4f Combine like terms: -4f + 4f = 0 5c + 0 = 0 + 4f 5c = 0 + 4f Remove the zero: 5c = 4f Divide each side by '5'. c = 0.8f Simplifying c = 0.8fSubproblem 2
Set the factor '(5c + 3f)' equal to zero and attempt to solve: Simplifying 5c + 3f = 0 Solving 5c + 3f = 0 Move all terms containing c to the left, all other terms to the right. Add '-3f' to each side of the equation. 5c + 3f + -3f = 0 + -3f Combine like terms: 3f + -3f = 0 5c + 0 = 0 + -3f 5c = 0 + -3f Remove the zero: 5c = -3f Divide each side by '5'. c = -0.6f Simplifying c = -0.6fSolution
c = {0.8f, -0.6f}
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