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Simplifying 35n2 + 85n + 30 = 0 Reorder the terms: 30 + 85n + 35n2 = 0 Solving 30 + 85n + 35n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '5'. 5(6 + 17n + 7n2) = 0 Factor a trinomial. 5((2 + n)(3 + 7n)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + n)' equal to zero and attempt to solve: Simplifying 2 + n = 0 Solving 2 + n = 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 + n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + n = 0 + -2 n = 0 + -2 Combine like terms: 0 + -2 = -2 n = -2 Simplifying n = -2Subproblem 2
Set the factor '(3 + 7n)' equal to zero and attempt to solve: Simplifying 3 + 7n = 0 Solving 3 + 7n = 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 + 7n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7n = 0 + -3 7n = 0 + -3 Combine like terms: 0 + -3 = -3 7n = -3 Divide each side by '7'. n = -0.4285714286 Simplifying n = -0.4285714286Solution
n = {-2, -0.4285714286}
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