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Simplifying 5n2 + 33n + -21 = n Reorder the terms: -21 + 33n + 5n2 = n Solving -21 + 33n + 5n2 = n Solving for variable 'n'. Reorder the terms: -21 + 33n + -1n + 5n2 = n + -1n Combine like terms: 33n + -1n = 32n -21 + 32n + 5n2 = n + -1n Combine like terms: n + -1n = 0 -21 + 32n + 5n2 = 0 Factor a trinomial. (-7 + -1n)(3 + -5n) = 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 '(3 + -5n)' equal to zero and attempt to solve: Simplifying 3 + -5n = 0 Solving 3 + -5n = 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 + -5n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5n = 0 + -3 -5n = 0 + -3 Combine like terms: 0 + -3 = -3 -5n = -3 Divide each side by '-5'. n = 0.6 Simplifying n = 0.6Solution
n = {-7, 0.6}
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