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Simplifying 3n2 + 64 = -32n Reorder the terms: 64 + 3n2 = -32n Solving 64 + 3n2 = -32n Solving for variable 'n'. Reorder the terms: 64 + 32n + 3n2 = -32n + 32n Combine like terms: -32n + 32n = 0 64 + 32n + 3n2 = 0 Factor a trinomial. (8 + n)(8 + 3n) = 0Subproblem 1
Set the factor '(8 + n)' equal to zero and attempt to solve: Simplifying 8 + n = 0 Solving 8 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + n = 0 + -8 n = 0 + -8 Combine like terms: 0 + -8 = -8 n = -8 Simplifying n = -8Subproblem 2
Set the factor '(8 + 3n)' equal to zero and attempt to solve: Simplifying 8 + 3n = 0 Solving 8 + 3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 3n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3n = 0 + -8 3n = 0 + -8 Combine like terms: 0 + -8 = -8 3n = -8 Divide each side by '3'. n = -2.666666667 Simplifying n = -2.666666667Solution
n = {-8, -2.666666667}
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