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Simplifying (3c + -5)(8c + -1) = 0 Reorder the terms: (-5 + 3c)(8c + -1) = 0 Reorder the terms: (-5 + 3c)(-1 + 8c) = 0 Multiply (-5 + 3c) * (-1 + 8c) (-5(-1 + 8c) + 3c * (-1 + 8c)) = 0 ((-1 * -5 + 8c * -5) + 3c * (-1 + 8c)) = 0 ((5 + -40c) + 3c * (-1 + 8c)) = 0 (5 + -40c + (-1 * 3c + 8c * 3c)) = 0 (5 + -40c + (-3c + 24c2)) = 0 Combine like terms: -40c + -3c = -43c (5 + -43c + 24c2) = 0 Solving 5 + -43c + 24c2 = 0 Solving for variable 'c'. Factor a trinomial. (1 + -8c)(5 + -3c) = 0Subproblem 1
Set the factor '(1 + -8c)' equal to zero and attempt to solve: Simplifying 1 + -8c = 0 Solving 1 + -8c = 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 + -8c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8c = 0 + -1 -8c = 0 + -1 Combine like terms: 0 + -1 = -1 -8c = -1 Divide each side by '-8'. c = 0.125 Simplifying c = 0.125Subproblem 2
Set the factor '(5 + -3c)' equal to zero and attempt to solve: Simplifying 5 + -3c = 0 Solving 5 + -3c = 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 + -3c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3c = 0 + -5 -3c = 0 + -5 Combine like terms: 0 + -5 = -5 -3c = -5 Divide each side by '-3'. c = 1.666666667 Simplifying c = 1.666666667Solution
c = {0.125, 1.666666667}
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