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Simplifying (4b + 3c)(5b + 2c) = 0 Multiply (4b + 3c) * (5b + 2c) (4b * (5b + 2c) + 3c * (5b + 2c)) = 0 ((5b * 4b + 2c * 4b) + 3c * (5b + 2c)) = 0 Reorder the terms: ((8bc + 20b2) + 3c * (5b + 2c)) = 0 ((8bc + 20b2) + 3c * (5b + 2c)) = 0 (8bc + 20b2 + (5b * 3c + 2c * 3c)) = 0 (8bc + 20b2 + (15bc + 6c2)) = 0 Reorder the terms: (8bc + 15bc + 20b2 + 6c2) = 0 Combine like terms: 8bc + 15bc = 23bc (23bc + 20b2 + 6c2) = 0 Solving 23bc + 20b2 + 6c2 = 0 Solving for variable 'b'. Factor a trinomial. (5b + 2c)(4b + 3c) = 0Subproblem 1
Set the factor '(5b + 2c)' equal to zero and attempt to solve: Simplifying 5b + 2c = 0 Solving 5b + 2c = 0 Move all terms containing b to the left, all other terms to the right. Add '-2c' to each side of the equation. 5b + 2c + -2c = 0 + -2c Combine like terms: 2c + -2c = 0 5b + 0 = 0 + -2c 5b = 0 + -2c Remove the zero: 5b = -2c Divide each side by '5'. b = -0.4c Simplifying b = -0.4cSubproblem 2
Set the factor '(4b + 3c)' equal to zero and attempt to solve: Simplifying 4b + 3c = 0 Solving 4b + 3c = 0 Move all terms containing b to the left, all other terms to the right. Add '-3c' to each side of the equation. 4b + 3c + -3c = 0 + -3c Combine like terms: 3c + -3c = 0 4b + 0 = 0 + -3c 4b = 0 + -3c Remove the zero: 4b = -3c Divide each side by '4'. b = -0.75c Simplifying b = -0.75cSolution
b = {-0.4c, -0.75c}
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