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Simplifying 20b2 + 13br + -15r2 = 0 Reorder the terms: 13br + 20b2 + -15r2 = 0 Solving 13br + 20b2 + -15r2 = 0 Solving for variable 'b'. Factor a trinomial. (5b + -3r)(4b + 5r) = 0Subproblem 1
Set the factor '(5b + -3r)' equal to zero and attempt to solve: Simplifying 5b + -3r = 0 Solving 5b + -3r = 0 Move all terms containing b to the left, all other terms to the right. Add '3r' to each side of the equation. 5b + -3r + 3r = 0 + 3r Combine like terms: -3r + 3r = 0 5b + 0 = 0 + 3r 5b = 0 + 3r Remove the zero: 5b = 3r Divide each side by '5'. b = 0.6r Simplifying b = 0.6rSubproblem 2
Set the factor '(4b + 5r)' equal to zero and attempt to solve: Simplifying 4b + 5r = 0 Solving 4b + 5r = 0 Move all terms containing b to the left, all other terms to the right. Add '-5r' to each side of the equation. 4b + 5r + -5r = 0 + -5r Combine like terms: 5r + -5r = 0 4b + 0 = 0 + -5r 4b = 0 + -5r Remove the zero: 4b = -5r Divide each side by '4'. b = -1.25r Simplifying b = -1.25rSolution
b = {0.6r, -1.25r}
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