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Simplifying 12c2 + -128c + 180 = 0 Reorder the terms: 180 + -128c + 12c2 = 0 Solving 180 + -128c + 12c2 = 0 Solving for variable 'c'. Factor out the Greatest Common Factor (GCF), '4'. 4(45 + -32c + 3c2) = 0 Factor a trinomial. 4((5 + -3c)(9 + -1c)) = 0 Ignore the factor 4.Subproblem 1
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 = 1.666666667Subproblem 2
Set the factor '(9 + -1c)' equal to zero and attempt to solve: Simplifying 9 + -1c = 0 Solving 9 + -1c = 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 + -1c = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1c = 0 + -9 -1c = 0 + -9 Combine like terms: 0 + -9 = -9 -1c = -9 Divide each side by '-1'. c = 9 Simplifying c = 9Solution
c = {1.666666667, 9}
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