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Simplifying 9n2 + -42n + -162 = 21n Reorder the terms: -162 + -42n + 9n2 = 21n Solving -162 + -42n + 9n2 = 21n Solving for variable 'n'. Reorder the terms: -162 + -42n + -21n + 9n2 = 21n + -21n Combine like terms: -42n + -21n = -63n -162 + -63n + 9n2 = 21n + -21n Combine like terms: 21n + -21n = 0 -162 + -63n + 9n2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-18 + -7n + n2) = 0 Factor a trinomial. 9((-2 + -1n)(9 + -1n)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve: Simplifying -2 + -1n = 0 Solving -2 + -1n = 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 + -1n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1n = 0 + 2 -1n = 0 + 2 Combine like terms: 0 + 2 = 2 -1n = 2 Divide each side by '-1'. n = -2 Simplifying n = -2Subproblem 2
Set the factor '(9 + -1n)' equal to zero and attempt to solve: Simplifying 9 + -1n = 0 Solving 9 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1n = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1n = 0 + -9 -1n = 0 + -9 Combine like terms: 0 + -9 = -9 -1n = -9 Divide each side by '-1'. n = 9 Simplifying n = 9Solution
n = {-2, 9}
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