6=n^2+3n-12

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Solution for 6=n^2+3n-12 equation:


Simplifying
6 = n2 + 3n + -12

Reorder the terms:
6 = -12 + 3n + n2

Solving
6 = -12 + 3n + n2

Solving for variable 'n'.

Combine like terms: 6 + 12 = 18
18 + -3n + -1n2 = -12 + 3n + n2 + 12 + -3n + -1n2

Reorder the terms:
18 + -3n + -1n2 = -12 + 12 + 3n + -3n + n2 + -1n2

Combine like terms: -12 + 12 = 0
18 + -3n + -1n2 = 0 + 3n + -3n + n2 + -1n2
18 + -3n + -1n2 = 3n + -3n + n2 + -1n2

Combine like terms: 3n + -3n = 0
18 + -3n + -1n2 = 0 + n2 + -1n2
18 + -3n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
18 + -3n + -1n2 = 0

Factor a trinomial.
(3 + -1n)(6 + n) = 0

Subproblem 1

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 = 3

Subproblem 2

Set the factor '(6 + n)' equal to zero and attempt to solve: Simplifying 6 + n = 0 Solving 6 + n = 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 + n = 0 + -6 Combine like terms: 6 + -6 = 0 0 + n = 0 + -6 n = 0 + -6 Combine like terms: 0 + -6 = -6 n = -6 Simplifying n = -6

Solution

n = {3, -6}

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