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Simplifying 32c2 + -20c + 24c + -15 = 0 Reorder the terms: -15 + -20c + 24c + 32c2 = 0 Combine like terms: -20c + 24c = 4c -15 + 4c + 32c2 = 0 Solving -15 + 4c + 32c2 = 0 Solving for variable 'c'. Factor a trinomial. (-3 + -4c)(5 + -8c) = 0Subproblem 1
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 = -0.75Subproblem 2
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 = 0.625Solution
c = {-0.75, 0.625}
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