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Simplifying 15n2 + -32np + -7p2 = 0 Reorder the terms: -32np + 15n2 + -7p2 = 0 Solving -32np + 15n2 + -7p2 = 0 Solving for variable 'n'. Factor a trinomial. (3n + -7p)(5n + p) = 0Subproblem 1
Set the factor '(3n + -7p)' equal to zero and attempt to solve: Simplifying 3n + -7p = 0 Solving 3n + -7p = 0 Move all terms containing n to the left, all other terms to the right. Add '7p' to each side of the equation. 3n + -7p + 7p = 0 + 7p Combine like terms: -7p + 7p = 0 3n + 0 = 0 + 7p 3n = 0 + 7p Remove the zero: 3n = 7p Divide each side by '3'. n = 2.333333333p Simplifying n = 2.333333333pSubproblem 2
Set the factor '(5n + p)' equal to zero and attempt to solve: Simplifying 5n + p = 0 Solving 5n + p = 0 Move all terms containing n to the left, all other terms to the right. Add '-1p' to each side of the equation. 5n + p + -1p = 0 + -1p Combine like terms: p + -1p = 0 5n + 0 = 0 + -1p 5n = 0 + -1p Remove the zero: 5n = -1p Divide each side by '5'. n = -0.2p Simplifying n = -0.2pSolution
n = {2.333333333p, -0.2p}
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