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Simplifying b2c3 + 8bc4 + 12c5 = 0 Reorder the terms: 8bc4 + b2c3 + 12c5 = 0 Solving 8bc4 + b2c3 + 12c5 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), 'c3'. c3(8bc + b2 + 12c2) = 0 Factor a trinomial. c3((b + 2c)(b + 6c)) = 0Subproblem 1
Set the factor 'c3' equal to zero and attempt to solve: Simplifying c3 = 0 Solving c3 = 0 Move all terms containing b to the left, all other terms to the right. Add '-1c3' to each side of the equation. c3 + -1c3 = 0 + -1c3 Remove the zero: 0 = -1c3 Simplifying 0 = -1c3 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 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 = -2cSubproblem 3
Set the factor '(b + 6c)' equal to zero and attempt to solve: Simplifying b + 6c = 0 Solving b + 6c = 0 Move all terms containing b to the left, all other terms to the right. Add '-6c' to each side of the equation. b + 6c + -6c = 0 + -6c Combine like terms: 6c + -6c = 0 b + 0 = 0 + -6c b = 0 + -6c Remove the zero: b = -6c Simplifying b = -6cSolution
b = {-2c, -6c}
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