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Simplifying 2n2 = -7n + 30 Reorder the terms: 2n2 = 30 + -7n Solving 2n2 = 30 + -7n Solving for variable 'n'. Reorder the terms: -30 + 7n + 2n2 = 30 + -7n + -30 + 7n Reorder the terms: -30 + 7n + 2n2 = 30 + -30 + -7n + 7n Combine like terms: 30 + -30 = 0 -30 + 7n + 2n2 = 0 + -7n + 7n -30 + 7n + 2n2 = -7n + 7n Combine like terms: -7n + 7n = 0 -30 + 7n + 2n2 = 0 Factor a trinomial. (-6 + -1n)(5 + -2n) = 0Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve: Simplifying -6 + -1n = 0 Solving -6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1n = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1n = 0 + 6 -1n = 0 + 6 Combine like terms: 0 + 6 = 6 -1n = 6 Divide each side by '-1'. n = -6 Simplifying n = -6Subproblem 2
Set the factor '(5 + -2n)' equal to zero and attempt to solve: Simplifying 5 + -2n = 0 Solving 5 + -2n = 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 + -2n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2n = 0 + -5 -2n = 0 + -5 Combine like terms: 0 + -5 = -5 -2n = -5 Divide each side by '-2'. n = 2.5 Simplifying n = 2.5Solution
n = {-6, 2.5}
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