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Simplifying 0 = -6b2 + -9bc + 6c2 Reorder the terms: 0 = -9bc + -6b2 + 6c2 Solving 0 = -9bc + -6b2 + 6c2 Solving for variable 'b'. Remove the zero: 9bc + 6b2 + -6c2 = -9bc + -6b2 + 6c2 + 9bc + 6b2 + -6c2 Reorder the terms: 9bc + 6b2 + -6c2 = -9bc + 9bc + -6b2 + 6b2 + 6c2 + -6c2 Combine like terms: -9bc + 9bc = 0 9bc + 6b2 + -6c2 = 0 + -6b2 + 6b2 + 6c2 + -6c2 9bc + 6b2 + -6c2 = -6b2 + 6b2 + 6c2 + -6c2 Combine like terms: -6b2 + 6b2 = 0 9bc + 6b2 + -6c2 = 0 + 6c2 + -6c2 9bc + 6b2 + -6c2 = 6c2 + -6c2 Combine like terms: 6c2 + -6c2 = 0 9bc + 6b2 + -6c2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3bc + 2b2 + -2c2) = 0 Factor a trinomial. 3((2b + -1c)(b + 2c)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2b + -1c)' equal to zero and attempt to solve: Simplifying 2b + -1c = 0 Solving 2b + -1c = 0 Move all terms containing b to the left, all other terms to the right. Add 'c' to each side of the equation. 2b + -1c + c = 0 + c Combine like terms: -1c + c = 0 2b + 0 = 0 + c 2b = 0 + c Remove the zero: 2b = c Divide each side by '2'. b = 0.5c Simplifying b = 0.5cSubproblem 2
Set the factor '(b + 2c)' equal to zero and attempt to solve: Simplifying b + 2c = 0 Solving b + 2c = 0 Move all terms containing b to the left, all other terms to the right. Add '-2c' to each side of the equation. b + 2c + -2c = 0 + -2c Combine like terms: 2c + -2c = 0 b + 0 = 0 + -2c b = 0 + -2c Remove the zero: b = -2c Simplifying b = -2cSolution
b = {0.5c, -2c}
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