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Simplifying 8n2 + -10np + -3p2 = 0 Reorder the terms: -10np + 8n2 + -3p2 = 0 Solving -10np + 8n2 + -3p2 = 0 Solving for variable 'n'. Factor a trinomial. (2n + -3p)(4n + p) = 0Subproblem 1
Set the factor '(2n + -3p)' equal to zero and attempt to solve: Simplifying 2n + -3p = 0 Solving 2n + -3p = 0 Move all terms containing n to the left, all other terms to the right. Add '3p' to each side of the equation. 2n + -3p + 3p = 0 + 3p Combine like terms: -3p + 3p = 0 2n + 0 = 0 + 3p 2n = 0 + 3p Remove the zero: 2n = 3p Divide each side by '2'. n = 1.5p Simplifying n = 1.5pSubproblem 2
Set the factor '(4n + p)' equal to zero and attempt to solve: Simplifying 4n + p = 0 Solving 4n + p = 0 Move all terms containing n to the left, all other terms to the right. Add '-1p' to each side of the equation. 4n + p + -1p = 0 + -1p Combine like terms: p + -1p = 0 4n + 0 = 0 + -1p 4n = 0 + -1p Remove the zero: 4n = -1p Divide each side by '4'. n = -0.25p Simplifying n = -0.25pSolution
n = {1.5p, -0.25p}
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