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Simplifying 3c2 + 9c + -8 + c + -5 + 12c2 + -6c + 10 = 0 Reorder the terms: -8 + -5 + 10 + 9c + c + -6c + 3c2 + 12c2 = 0 Combine like terms: -8 + -5 = -13 -13 + 10 + 9c + c + -6c + 3c2 + 12c2 = 0 Combine like terms: -13 + 10 = -3 -3 + 9c + c + -6c + 3c2 + 12c2 = 0 Combine like terms: 9c + c = 10c -3 + 10c + -6c + 3c2 + 12c2 = 0 Combine like terms: 10c + -6c = 4c -3 + 4c + 3c2 + 12c2 = 0 Combine like terms: 3c2 + 12c2 = 15c2 -3 + 4c + 15c2 = 0 Solving -3 + 4c + 15c2 = 0 Solving for variable 'c'. Factor a trinomial. (-3 + -5c)(1 + -3c) = 0Subproblem 1
Set the factor '(-3 + -5c)' equal to zero and attempt to solve: Simplifying -3 + -5c = 0 Solving -3 + -5c = 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 + -5c = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5c = 0 + 3 -5c = 0 + 3 Combine like terms: 0 + 3 = 3 -5c = 3 Divide each side by '-5'. c = -0.6 Simplifying c = -0.6Subproblem 2
Set the factor '(1 + -3c)' equal to zero and attempt to solve: Simplifying 1 + -3c = 0 Solving 1 + -3c = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3c = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3c = 0 + -1 -3c = 0 + -1 Combine like terms: 0 + -1 = -1 -3c = -1 Divide each side by '-3'. c = 0.3333333333 Simplifying c = 0.3333333333Solution
c = {-0.6, 0.3333333333}
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