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Simplifying (5b + -4c)(3b + -2c) = 0 Multiply (5b + -4c) * (3b + -2c) (5b * (3b + -2c) + -4c * (3b + -2c)) = 0 ((3b * 5b + -2c * 5b) + -4c * (3b + -2c)) = 0 Reorder the terms: ((-10bc + 15b2) + -4c * (3b + -2c)) = 0 ((-10bc + 15b2) + -4c * (3b + -2c)) = 0 (-10bc + 15b2 + (3b * -4c + -2c * -4c)) = 0 (-10bc + 15b2 + (-12bc + 8c2)) = 0 Reorder the terms: (-10bc + -12bc + 15b2 + 8c2) = 0 Combine like terms: -10bc + -12bc = -22bc (-22bc + 15b2 + 8c2) = 0 Solving -22bc + 15b2 + 8c2 = 0 Solving for variable 'b'. Factor a trinomial. (5b + -4c)(3b + -2c) = 0Subproblem 1
Set the factor '(5b + -4c)' equal to zero and attempt to solve: Simplifying 5b + -4c = 0 Solving 5b + -4c = 0 Move all terms containing b to the left, all other terms to the right. Add '4c' to each side of the equation. 5b + -4c + 4c = 0 + 4c Combine like terms: -4c + 4c = 0 5b + 0 = 0 + 4c 5b = 0 + 4c Remove the zero: 5b = 4c Divide each side by '5'. b = 0.8c Simplifying b = 0.8cSubproblem 2
Set the factor '(3b + -2c)' equal to zero and attempt to solve: Simplifying 3b + -2c = 0 Solving 3b + -2c = 0 Move all terms containing b to the left, all other terms to the right. Add '2c' to each side of the equation. 3b + -2c + 2c = 0 + 2c Combine like terms: -2c + 2c = 0 3b + 0 = 0 + 2c 3b = 0 + 2c Remove the zero: 3b = 2c Divide each side by '3'. b = 0.6666666667c Simplifying b = 0.6666666667cSolution
b = {0.8c, 0.6666666667c}
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