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Simplifying (2b + 5c)(3b + 8c) = 0 Multiply (2b + 5c) * (3b + 8c) (2b * (3b + 8c) + 5c * (3b + 8c)) = 0 ((3b * 2b + 8c * 2b) + 5c * (3b + 8c)) = 0 Reorder the terms: ((16bc + 6b2) + 5c * (3b + 8c)) = 0 ((16bc + 6b2) + 5c * (3b + 8c)) = 0 (16bc + 6b2 + (3b * 5c + 8c * 5c)) = 0 (16bc + 6b2 + (15bc + 40c2)) = 0 Reorder the terms: (16bc + 15bc + 6b2 + 40c2) = 0 Combine like terms: 16bc + 15bc = 31bc (31bc + 6b2 + 40c2) = 0 Solving 31bc + 6b2 + 40c2 = 0 Solving for variable 'b'. Factor a trinomial. (2b + 5c)(3b + 8c) = 0Subproblem 1
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 = -2.5cSubproblem 2
Set the factor '(3b + 8c)' equal to zero and attempt to solve: Simplifying 3b + 8c = 0 Solving 3b + 8c = 0 Move all terms containing b to the left, all other terms to the right. Add '-8c' to each side of the equation. 3b + 8c + -8c = 0 + -8c Combine like terms: 8c + -8c = 0 3b + 0 = 0 + -8c 3b = 0 + -8c Remove the zero: 3b = -8c Divide each side by '3'. b = -2.666666667c Simplifying b = -2.666666667cSolution
b = {-2.5c, -2.666666667c}
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