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Simplifying 36c2 + -33cb + -45b2 = 0 Reorder the terms: -33bc + -45b2 + 36c2 = 0 Solving -33bc + -45b2 + 36c2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '3'. 3(-11bc + -15b2 + 12c2) = 0 Factor a trinomial. 3((-3b + -4c)(5b + -3c)) = 0 Ignore the factor 3.Subproblem 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 '(5b + -3c)' equal to zero and attempt to solve: Simplifying 5b + -3c = 0 Solving 5b + -3c = 0 Move all terms containing b to the left, all other terms to the right. Add '3c' to each side of the equation. 5b + -3c + 3c = 0 + 3c Combine like terms: -3c + 3c = 0 5b + 0 = 0 + 3c 5b = 0 + 3c Remove the zero: 5b = 3c Divide each side by '5'. b = 0.6c Simplifying b = 0.6cSolution
b = {-1.333333333c, 0.6c}
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