(n*n)+3n-12=6

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Solution for (n*n)+3n-12=6 equation:


Simplifying
(n * n) + 3n + -12 = 6

Multiply n * n
(n2) + 3n + -12 = 6
n2 + 3n + -12 = 6

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

Solving
-12 + 3n + n2 = 6

Solving for variable 'n'.

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

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

Combine like terms: 6 + -6 = 0
-18 + 3n + n2 = 0

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

Subproblem 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 = -6

Subproblem 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 = 3

Solution

n = {-6, 3}

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