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Simplifying 0 = c2 + -15c + 54 Reorder the terms: 0 = 54 + -15c + c2 Solving 0 = 54 + -15c + c2 Solving for variable 'c'. Combine like terms: 0 + -54 = -54 -54 + 15c + -1c2 = 54 + -15c + c2 + -54 + 15c + -1c2 Reorder the terms: -54 + 15c + -1c2 = 54 + -54 + -15c + 15c + c2 + -1c2 Combine like terms: 54 + -54 = 0 -54 + 15c + -1c2 = 0 + -15c + 15c + c2 + -1c2 -54 + 15c + -1c2 = -15c + 15c + c2 + -1c2 Combine like terms: -15c + 15c = 0 -54 + 15c + -1c2 = 0 + c2 + -1c2 -54 + 15c + -1c2 = c2 + -1c2 Combine like terms: c2 + -1c2 = 0 -54 + 15c + -1c2 = 0 Factor a trinomial. (-9 + c)(6 + -1c) = 0Subproblem 1
Set the factor '(-9 + c)' equal to zero and attempt to solve: Simplifying -9 + c = 0 Solving -9 + c = 0 Move all terms containing c to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + c = 0 + 9 Combine like terms: -9 + 9 = 0 0 + c = 0 + 9 c = 0 + 9 Combine like terms: 0 + 9 = 9 c = 9 Simplifying c = 9Subproblem 2
Set the factor '(6 + -1c)' equal to zero and attempt to solve: Simplifying 6 + -1c = 0 Solving 6 + -1c = 0 Move all terms containing c to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1c = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1c = 0 + -6 -1c = 0 + -6 Combine like terms: 0 + -6 = -6 -1c = -6 Divide each side by '-1'. c = 6 Simplifying c = 6Solution
c = {9, 6}
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