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Simplifying 15n2 + -13np + -20p2 = 0 Reorder the terms: -13np + 15n2 + -20p2 = 0 Solving -13np + 15n2 + -20p2 = 0 Solving for variable 'n'. Factor a trinomial. (3n + -5p)(5n + 4p) = 0Subproblem 1
Set the factor '(3n + -5p)' equal to zero and attempt to solve: Simplifying 3n + -5p = 0 Solving 3n + -5p = 0 Move all terms containing n to the left, all other terms to the right. Add '5p' to each side of the equation. 3n + -5p + 5p = 0 + 5p Combine like terms: -5p + 5p = 0 3n + 0 = 0 + 5p 3n = 0 + 5p Remove the zero: 3n = 5p Divide each side by '3'. n = 1.666666667p Simplifying n = 1.666666667pSubproblem 2
Set the factor '(5n + 4p)' equal to zero and attempt to solve: Simplifying 5n + 4p = 0 Solving 5n + 4p = 0 Move all terms containing n to the left, all other terms to the right. Add '-4p' to each side of the equation. 5n + 4p + -4p = 0 + -4p Combine like terms: 4p + -4p = 0 5n + 0 = 0 + -4p 5n = 0 + -4p Remove the zero: 5n = -4p Divide each side by '5'. n = -0.8p Simplifying n = -0.8pSolution
n = {1.666666667p, -0.8p}
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