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Simplifying 3n2 + 51n + 210 = 0 Reorder the terms: 210 + 51n + 3n2 = 0 Solving 210 + 51n + 3n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '3'. 3(70 + 17n + n2) = 0 Factor a trinomial. 3((10 + n)(7 + n)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(10 + n)' equal to zero and attempt to solve: Simplifying 10 + n = 0 Solving 10 + n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + n = 0 + -10 n = 0 + -10 Combine like terms: 0 + -10 = -10 n = -10 Simplifying n = -10Subproblem 2
Set the factor '(7 + n)' equal to zero and attempt to solve: Simplifying 7 + n = 0 Solving 7 + n = 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 + n = 0 + -7 Combine like terms: 7 + -7 = 0 0 + n = 0 + -7 n = 0 + -7 Combine like terms: 0 + -7 = -7 n = -7 Simplifying n = -7Solution
n = {-10, -7}
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