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Simplifying 6b2 + 23bc + 20c2 = 0 Reorder the terms: 23bc + 6b2 + 20c2 = 0 Solving 23bc + 6b2 + 20c2 = 0 Solving for variable 'b'. Factor a trinomial. (3b + 4c)(2b + 5c) = 0Subproblem 1
Set the factor '(3b + 4c)' equal to zero and attempt to solve: Simplifying 3b + 4c = 0 Solving 3b + 4c = 0 Move all terms containing b to the left, all other terms to the right. Add '-4c' to each side of the equation. 3b + 4c + -4c = 0 + -4c Combine like terms: 4c + -4c = 0 3b + 0 = 0 + -4c 3b = 0 + -4c Remove the zero: 3b = -4c Divide each side by '3'. b = -1.333333333c Simplifying b = -1.333333333cSubproblem 2
Set the factor '(2b + 5c)' equal to zero and attempt to solve: Simplifying 2b + 5c = 0 Solving 2b + 5c = 0 Move all terms containing b to the left, all other terms to the right. Add '-5c' to each side of the equation. 2b + 5c + -5c = 0 + -5c Combine like terms: 5c + -5c = 0 2b + 0 = 0 + -5c 2b = 0 + -5c Remove the zero: 2b = -5c Divide each side by '2'. b = -2.5c Simplifying b = -2.5cSolution
b = {-1.333333333c, -2.5c}
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