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Simplifying 2n2 = n + 21 Reorder the terms: 2n2 = 21 + n Solving 2n2 = 21 + n Solving for variable 'n'. Reorder the terms: -21 + -1n + 2n2 = 21 + n + -21 + -1n Reorder the terms: -21 + -1n + 2n2 = 21 + -21 + n + -1n Combine like terms: 21 + -21 = 0 -21 + -1n + 2n2 = 0 + n + -1n -21 + -1n + 2n2 = n + -1n Combine like terms: n + -1n = 0 -21 + -1n + 2n2 = 0 Factor a trinomial. (-3 + -1n)(7 + -2n) = 0Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve: Simplifying -3 + -1n = 0 Solving -3 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1n = 0 + 3 -1n = 0 + 3 Combine like terms: 0 + 3 = 3 -1n = 3 Divide each side by '-1'. n = -3 Simplifying n = -3Subproblem 2
Set the factor '(7 + -2n)' equal to zero and attempt to solve: Simplifying 7 + -2n = 0 Solving 7 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2n = 0 + -7 -2n = 0 + -7 Combine like terms: 0 + -7 = -7 -2n = -7 Divide each side by '-2'. n = 3.5 Simplifying n = 3.5Solution
n = {-3, 3.5}
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