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Simplifying 12n2 + -5np + -2p2 = 0 Reorder the terms: -5np + 12n2 + -2p2 = 0 Solving -5np + 12n2 + -2p2 = 0 Solving for variable 'n'. Factor a trinomial. (3n + -2p)(4n + p) = 0Subproblem 1
Set the factor '(3n + -2p)' equal to zero and attempt to solve: Simplifying 3n + -2p = 0 Solving 3n + -2p = 0 Move all terms containing n to the left, all other terms to the right. Add '2p' to each side of the equation. 3n + -2p + 2p = 0 + 2p Combine like terms: -2p + 2p = 0 3n + 0 = 0 + 2p 3n = 0 + 2p Remove the zero: 3n = 2p Divide each side by '3'. n = 0.6666666667p Simplifying n = 0.6666666667pSubproblem 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 = {0.6666666667p, -0.25p}
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