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Simplifying 5n2 = 128 + -12n Solving 5n2 = 128 + -12n Solving for variable 'n'. Reorder the terms: -128 + 12n + 5n2 = 128 + -12n + -128 + 12n Reorder the terms: -128 + 12n + 5n2 = 128 + -128 + -12n + 12n Combine like terms: 128 + -128 = 0 -128 + 12n + 5n2 = 0 + -12n + 12n -128 + 12n + 5n2 = -12n + 12n Combine like terms: -12n + 12n = 0 -128 + 12n + 5n2 = 0 Factor a trinomial. (-32 + -5n)(4 + -1n) = 0Subproblem 1
Set the factor '(-32 + -5n)' equal to zero and attempt to solve: Simplifying -32 + -5n = 0 Solving -32 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + -5n = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -5n = 0 + 32 -5n = 0 + 32 Combine like terms: 0 + 32 = 32 -5n = 32 Divide each side by '-5'. n = -6.4 Simplifying n = -6.4Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Solution
n = {-6.4, 4}
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