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Simplifying (4c + -5)(5c + 1) = 0 Reorder the terms: (-5 + 4c)(5c + 1) = 0 Reorder the terms: (-5 + 4c)(1 + 5c) = 0 Multiply (-5 + 4c) * (1 + 5c) (-5(1 + 5c) + 4c * (1 + 5c)) = 0 ((1 * -5 + 5c * -5) + 4c * (1 + 5c)) = 0 ((-5 + -25c) + 4c * (1 + 5c)) = 0 (-5 + -25c + (1 * 4c + 5c * 4c)) = 0 (-5 + -25c + (4c + 20c2)) = 0 Combine like terms: -25c + 4c = -21c (-5 + -21c + 20c2) = 0 Solving -5 + -21c + 20c2 = 0 Solving for variable 'c'. Factor a trinomial. (-1 + -5c)(5 + -4c) = 0Subproblem 1
Set the factor '(-1 + -5c)' equal to zero and attempt to solve: Simplifying -1 + -5c = 0 Solving -1 + -5c = 0 Move all terms containing c to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -5c = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5c = 0 + 1 -5c = 0 + 1 Combine like terms: 0 + 1 = 1 -5c = 1 Divide each side by '-5'. c = -0.2 Simplifying c = -0.2Subproblem 2
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 = 1.25Solution
c = {-0.2, 1.25}
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