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Simplifying (4c + -1)(5c + 3) = 0 Reorder the terms: (-1 + 4c)(5c + 3) = 0 Reorder the terms: (-1 + 4c)(3 + 5c) = 0 Multiply (-1 + 4c) * (3 + 5c) (-1(3 + 5c) + 4c * (3 + 5c)) = 0 ((3 * -1 + 5c * -1) + 4c * (3 + 5c)) = 0 ((-3 + -5c) + 4c * (3 + 5c)) = 0 (-3 + -5c + (3 * 4c + 5c * 4c)) = 0 (-3 + -5c + (12c + 20c2)) = 0 Combine like terms: -5c + 12c = 7c (-3 + 7c + 20c2) = 0 Solving -3 + 7c + 20c2 = 0 Solving for variable 'c'. Factor a trinomial. (-3 + -5c)(1 + -4c) = 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 '(1 + -4c)' equal to zero and attempt to solve: Simplifying 1 + -4c = 0 Solving 1 + -4c = 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 + -4c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4c = 0 + -1 -4c = 0 + -1 Combine like terms: 0 + -1 = -1 -4c = -1 Divide each side by '-4'. c = 0.25 Simplifying c = 0.25Solution
c = {-0.6, 0.25}
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