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Simplifying 5n2 + 36 = 12n + 4n2 Reorder the terms: 36 + 5n2 = 12n + 4n2 Solving 36 + 5n2 = 12n + 4n2 Solving for variable 'n'. Reorder the terms: 36 + -12n + 5n2 + -4n2 = 12n + 4n2 + -12n + -4n2 Combine like terms: 5n2 + -4n2 = 1n2 36 + -12n + 1n2 = 12n + 4n2 + -12n + -4n2 Reorder the terms: 36 + -12n + 1n2 = 12n + -12n + 4n2 + -4n2 Combine like terms: 12n + -12n = 0 36 + -12n + 1n2 = 0 + 4n2 + -4n2 36 + -12n + 1n2 = 4n2 + -4n2 Combine like terms: 4n2 + -4n2 = 0 36 + -12n + 1n2 = 0 Factor a trinomial. (6 + -1n)(6 + -1n) = 0Subproblem 1
Set the factor '(6 + -1n)' equal to zero and attempt to solve: Simplifying 6 + -1n = 0 Solving 6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1n = 0 + -6 -1n = 0 + -6 Combine like terms: 0 + -6 = -6 -1n = -6 Divide each side by '-1'. n = 6 Simplifying n = 6Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve: Simplifying 6 + -1n = 0 Solving 6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1n = 0 + -6 -1n = 0 + -6 Combine like terms: 0 + -6 = -6 -1n = -6 Divide each side by '-1'. n = 6 Simplifying n = 6Solution
n = {6, 6}
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