3n(n-6)=-28+n

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Solution for 3n(n-6)=-28+n equation:


Simplifying
3n(n + -6) = -28 + n

Reorder the terms:
3n(-6 + n) = -28 + n
(-6 * 3n + n * 3n) = -28 + n
(-18n + 3n2) = -28 + n

Solving
-18n + 3n2 = -28 + n

Solving for variable 'n'.

Reorder the terms:
28 + -18n + -1n + 3n2 = -28 + n + 28 + -1n

Combine like terms: -18n + -1n = -19n
28 + -19n + 3n2 = -28 + n + 28 + -1n

Reorder the terms:
28 + -19n + 3n2 = -28 + 28 + n + -1n

Combine like terms: -28 + 28 = 0
28 + -19n + 3n2 = 0 + n + -1n
28 + -19n + 3n2 = n + -1n

Combine like terms: n + -1n = 0
28 + -19n + 3n2 = 0

Factor a trinomial.
(7 + -3n)(4 + -1n) = 0


Subproblem 1
Set the factor '(7 + -3n)' equal to zero and attempt to solve:

Simplifying
7 + -3n = 0

Solving
7 + -3n = 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 + -3n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3n = 0 + -7
-3n = 0 + -7

Combine like terms: 0 + -7 = -7
-3n = -7

Divide each side by '-3'.
n = 2.333333333

Simplifying
n = 2.333333333

Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 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 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {2.333333333, 4}

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