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Simplifying 21N2 + 91N + -70 = 0 Reorder the terms: -70 + 91N + 21N2 = 0 Solving -70 + 91N + 21N2 = 0 Solving for variable 'N'. Factor out the Greatest Common Factor (GCF), '7'. 7(-10 + 13N + 3N2) = 0 Factor a trinomial. 7((-5 + -1N)(2 + -3N)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-5 + -1N)' equal to zero and attempt to solve: Simplifying -5 + -1N = 0 Solving -5 + -1N = 0 Move all terms containing N to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1N = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1N = 0 + 5 -1N = 0 + 5 Combine like terms: 0 + 5 = 5 -1N = 5 Divide each side by '-1'. N = -5 Simplifying N = -5Subproblem 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 = {-5, 0.6666666667}
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