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Simplifying (8c + 5)(3c + -5) = 0 Reorder the terms: (5 + 8c)(3c + -5) = 0 Reorder the terms: (5 + 8c)(-5 + 3c) = 0 Multiply (5 + 8c) * (-5 + 3c) (5(-5 + 3c) + 8c * (-5 + 3c)) = 0 ((-5 * 5 + 3c * 5) + 8c * (-5 + 3c)) = 0 ((-25 + 15c) + 8c * (-5 + 3c)) = 0 (-25 + 15c + (-5 * 8c + 3c * 8c)) = 0 (-25 + 15c + (-40c + 24c2)) = 0 Combine like terms: 15c + -40c = -25c (-25 + -25c + 24c2) = 0 Solving -25 + -25c + 24c2 = 0 Solving for variable 'c'. Factor a trinomial. (-5 + -8c)(5 + -3c) = 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 '(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 = {-0.625, 1.666666667}
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