5n-20=n^2-n-12

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Solution for 5n-20=n^2-n-12 equation: 


Simplifying
5n + -20 = n2 + -1n + -12

Reorder the terms:
-20 + 5n = n2 + -1n + -12

Reorder the terms:
-20 + 5n = -12 + -1n + n2

Solving
-20 + 5n = -12 + -1n + n2

Solving for variable 'n'.

Reorder the terms:
-20 + 12 + 5n + n + -1n2 = -12 + -1n + n2 + 12 + n + -1n2

Combine like terms: -20 + 12 = -8
-8 + 5n + n + -1n2 = -12 + -1n + n2 + 12 + n + -1n2

Combine like terms: 5n + n = 6n
-8 + 6n + -1n2 = -12 + -1n + n2 + 12 + n + -1n2

Reorder the terms:
-8 + 6n + -1n2 = -12 + 12 + -1n + n + n2 + -1n2

Combine like terms: -12 + 12 = 0
-8 + 6n + -1n2 = 0 + -1n + n + n2 + -1n2
-8 + 6n + -1n2 = -1n + n + n2 + -1n2

Combine like terms: -1n + n = 0
-8 + 6n + -1n2 = 0 + n2 + -1n2
-8 + 6n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-8 + 6n + -1n2 = 0

Factor a trinomial.
(-4 + n)(2 + -1n) = 0


Subproblem 1
Set the factor '(-4 + n)' equal to zero and attempt to solve:

Simplifying
-4 + n = 0

Solving
-4 + n = 0

Move all terms containing n to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + n = 0 + 4
n = 0 + 4

Combine like terms: 0 + 4 = 4
n = 4

Simplifying
n = 4

Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {4, 2}

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