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Simplifying 6n2 + 84n + 294 = 0 Reorder the terms: 294 + 84n + 6n2 = 0 Solving 294 + 84n + 6n2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '6'. 6(49 + 14n + n2) = 0 Factor a trinomial. 6((7 + n)(7 + n)) = 0 Ignore the factor 6.Subproblem 1
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 = -7Subproblem 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 = {-7, -7}
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