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Simplifying 3n2 + 10n + -3 = 5 Reorder the terms: -3 + 10n + 3n2 = 5 Solving -3 + 10n + 3n2 = 5 Solving for variable 'n'. Reorder the terms: -3 + -5 + 10n + 3n2 = 5 + -5 Combine like terms: -3 + -5 = -8 -8 + 10n + 3n2 = 5 + -5 Combine like terms: 5 + -5 = 0 -8 + 10n + 3n2 = 0 Factor a trinomial. (-4 + -1n)(2 + -3n) = 0Subproblem 1
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 = -4Subproblem 2
Set the factor '(2 + -3n)' equal to zero and attempt to solve: Simplifying 2 + -3n = 0 Solving 2 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3n = 0 + -2 -3n = 0 + -2 Combine like terms: 0 + -2 = -2 -3n = -2 Divide each side by '-3'. n = 0.6666666667 Simplifying n = 0.6666666667Solution
n = {-4, 0.6666666667}
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