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Simplifying (4c + -1)(7c + -5) = 0 Reorder the terms: (-1 + 4c)(7c + -5) = 0 Reorder the terms: (-1 + 4c)(-5 + 7c) = 0 Multiply (-1 + 4c) * (-5 + 7c) (-1(-5 + 7c) + 4c * (-5 + 7c)) = 0 ((-5 * -1 + 7c * -1) + 4c * (-5 + 7c)) = 0 ((5 + -7c) + 4c * (-5 + 7c)) = 0 (5 + -7c + (-5 * 4c + 7c * 4c)) = 0 (5 + -7c + (-20c + 28c2)) = 0 Combine like terms: -7c + -20c = -27c (5 + -27c + 28c2) = 0 Solving 5 + -27c + 28c2 = 0 Solving for variable 'c'. Factor a trinomial. (1 + -4c)(5 + -7c) = 0Subproblem 1
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 = 0.25Subproblem 2
Set the factor '(5 + -7c)' equal to zero and attempt to solve: Simplifying 5 + -7c = 0 Solving 5 + -7c = 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 + -7c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7c = 0 + -5 -7c = 0 + -5 Combine like terms: 0 + -5 = -5 -7c = -5 Divide each side by '-7'. c = 0.7142857143 Simplifying c = 0.7142857143Solution
c = {0.25, 0.7142857143}
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