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Simplifying 0 = -3n2 + 7 + -20n Reorder the terms: 0 = 7 + -20n + -3n2 Solving 0 = 7 + -20n + -3n2 Solving for variable 'n'. Combine like terms: 0 + -7 = -7 -7 + 20n + 3n2 = 7 + -20n + -3n2 + -7 + 20n + 3n2 Reorder the terms: -7 + 20n + 3n2 = 7 + -7 + -20n + 20n + -3n2 + 3n2 Combine like terms: 7 + -7 = 0 -7 + 20n + 3n2 = 0 + -20n + 20n + -3n2 + 3n2 -7 + 20n + 3n2 = -20n + 20n + -3n2 + 3n2 Combine like terms: -20n + 20n = 0 -7 + 20n + 3n2 = 0 + -3n2 + 3n2 -7 + 20n + 3n2 = -3n2 + 3n2 Combine like terms: -3n2 + 3n2 = 0 -7 + 20n + 3n2 = 0 Factor a trinomial. (-7 + -1n)(1 + -3n) = 0Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve: Simplifying -7 + -1n = 0 Solving -7 + -1n = 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 + -1n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1n = 0 + 7 -1n = 0 + 7 Combine like terms: 0 + 7 = 7 -1n = 7 Divide each side by '-1'. n = -7 Simplifying n = -7Subproblem 2
Set the factor '(1 + -3n)' equal to zero and attempt to solve: Simplifying 1 + -3n = 0 Solving 1 + -3n = 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 + -3n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3n = 0 + -1 -3n = 0 + -1 Combine like terms: 0 + -1 = -1 -3n = -1 Divide each side by '-3'. n = 0.3333333333 Simplifying n = 0.3333333333Solution
n = {-7, 0.3333333333}
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