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Simplifying c2 + -2c = 24 + 3c Reorder the terms: -2c + c2 = 24 + 3c Solving -2c + c2 = 24 + 3c Solving for variable 'c'. Reorder the terms: -24 + -2c + -3c + c2 = 24 + 3c + -24 + -3c Combine like terms: -2c + -3c = -5c -24 + -5c + c2 = 24 + 3c + -24 + -3c Reorder the terms: -24 + -5c + c2 = 24 + -24 + 3c + -3c Combine like terms: 24 + -24 = 0 -24 + -5c + c2 = 0 + 3c + -3c -24 + -5c + c2 = 3c + -3c Combine like terms: 3c + -3c = 0 -24 + -5c + c2 = 0 Factor a trinomial. (-3 + -1c)(8 + -1c) = 0Subproblem 1
Set the factor '(-3 + -1c)' equal to zero and attempt to solve: Simplifying -3 + -1c = 0 Solving -3 + -1c = 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 + -1c = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1c = 0 + 3 -1c = 0 + 3 Combine like terms: 0 + 3 = 3 -1c = 3 Divide each side by '-1'. c = -3 Simplifying c = -3Subproblem 2
Set the factor '(8 + -1c)' equal to zero and attempt to solve: Simplifying 8 + -1c = 0 Solving 8 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1c = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1c = 0 + -8 -1c = 0 + -8 Combine like terms: 0 + -8 = -8 -1c = -8 Divide each side by '-1'. c = 8 Simplifying c = 8Solution
c = {-3, 8}
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