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Simplifying 3n2 + -20n + 4 = 7 + -4n2 Reorder the terms: 4 + -20n + 3n2 = 7 + -4n2 Solving 4 + -20n + 3n2 = 7 + -4n2 Solving for variable 'n'. Reorder the terms: 4 + -7 + -20n + 3n2 + 4n2 = 7 + -4n2 + -7 + 4n2 Combine like terms: 4 + -7 = -3 -3 + -20n + 3n2 + 4n2 = 7 + -4n2 + -7 + 4n2 Combine like terms: 3n2 + 4n2 = 7n2 -3 + -20n + 7n2 = 7 + -4n2 + -7 + 4n2 Reorder the terms: -3 + -20n + 7n2 = 7 + -7 + -4n2 + 4n2 Combine like terms: 7 + -7 = 0 -3 + -20n + 7n2 = 0 + -4n2 + 4n2 -3 + -20n + 7n2 = -4n2 + 4n2 Combine like terms: -4n2 + 4n2 = 0 -3 + -20n + 7n2 = 0 Factor a trinomial. (-1 + -7n)(3 + -1n) = 0Subproblem 1
Set the factor '(-1 + -7n)' equal to zero and attempt to solve: Simplifying -1 + -7n = 0 Solving -1 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -7n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -7n = 0 + 1 -7n = 0 + 1 Combine like terms: 0 + 1 = 1 -7n = 1 Divide each side by '-7'. n = -0.1428571429 Simplifying n = -0.1428571429Subproblem 2
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 = 3Solution
n = {-0.1428571429, 3}
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