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Simplifying (-8c + 5)(-4c + 3) = 0 Reorder the terms: (5 + -8c)(-4c + 3) = 0 Reorder the terms: (5 + -8c)(3 + -4c) = 0 Multiply (5 + -8c) * (3 + -4c) (5(3 + -4c) + -8c * (3 + -4c)) = 0 ((3 * 5 + -4c * 5) + -8c * (3 + -4c)) = 0 ((15 + -20c) + -8c * (3 + -4c)) = 0 (15 + -20c + (3 * -8c + -4c * -8c)) = 0 (15 + -20c + (-24c + 32c2)) = 0 Combine like terms: -20c + -24c = -44c (15 + -44c + 32c2) = 0 Solving 15 + -44c + 32c2 = 0 Solving for variable 'c'. Factor a trinomial. (5 + -8c)(3 + -4c) = 0Subproblem 1
Set the factor '(5 + -8c)' equal to zero and attempt to solve: Simplifying 5 + -8c = 0 Solving 5 + -8c = 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 + -8c = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8c = 0 + -5 -8c = 0 + -5 Combine like terms: 0 + -5 = -5 -8c = -5 Divide each side by '-8'. c = 0.625 Simplifying c = 0.625Subproblem 2
Set the factor '(3 + -4c)' equal to zero and attempt to solve: Simplifying 3 + -4c = 0 Solving 3 + -4c = 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 + -4c = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4c = 0 + -3 -4c = 0 + -3 Combine like terms: 0 + -3 = -3 -4c = -3 Divide each side by '-4'. c = 0.75 Simplifying c = 0.75Solution
c = {0.625, 0.75}
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