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Simplifying 16c2 + 10cb + -24cb + -15b2 = 0 Reorder the terms: 10bc + -24bc + -15b2 + 16c2 = 0 Combine like terms: 10bc + -24bc = -14bc -14bc + -15b2 + 16c2 = 0 Solving -14bc + -15b2 + 16c2 = 0 Solving for variable 'b'. Factor a trinomial. (-5b + -8c)(3b + -2c) = 0Subproblem 1
Set the factor '(-5b + -8c)' equal to zero and attempt to solve: Simplifying -5b + -8c = 0 Solving -5b + -8c = 0 Move all terms containing b to the left, all other terms to the right. Add '8c' to each side of the equation. -5b + -8c + 8c = 0 + 8c Combine like terms: -8c + 8c = 0 -5b + 0 = 0 + 8c -5b = 0 + 8c Remove the zero: -5b = 8c Divide each side by '-5'. b = -1.6c Simplifying b = -1.6cSubproblem 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 = {-1.6c, 0.6666666667c}
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