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Simplifying 6c2 = 9 + 15c Solving 6c2 = 9 + 15c Solving for variable 'c'. Reorder the terms: -9 + -15c + 6c2 = 9 + 15c + -9 + -15c Reorder the terms: -9 + -15c + 6c2 = 9 + -9 + 15c + -15c Combine like terms: 9 + -9 = 0 -9 + -15c + 6c2 = 0 + 15c + -15c -9 + -15c + 6c2 = 15c + -15c Combine like terms: 15c + -15c = 0 -9 + -15c + 6c2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + -5c + 2c2) = 0 Factor a trinomial. 3((-1 + -2c)(3 + -1c)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -2c)' equal to zero and attempt to solve: Simplifying -1 + -2c = 0 Solving -1 + -2c = 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 + -2c = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2c = 0 + 1 -2c = 0 + 1 Combine like terms: 0 + 1 = 1 -2c = 1 Divide each side by '-2'. c = -0.5 Simplifying c = -0.5Subproblem 2
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 = 3Solution
c = {-0.5, 3}
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