-3n(n-2)-(8+2n)=-6n

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Solution for -3n(n-2)-(8+2n)=-6n equation: 


Simplifying
-3n(n + -2) + -1(8 + 2n) = -6n

Reorder the terms:
-3n(-2 + n) + -1(8 + 2n) = -6n
(-2 * -3n + n * -3n) + -1(8 + 2n) = -6n
(6n + -3n2) + -1(8 + 2n) = -6n
6n + -3n2 + (8 * -1 + 2n * -1) = -6n
6n + -3n2 + (-8 + -2n) = -6n

Reorder the terms:
-8 + 6n + -2n + -3n2 = -6n

Combine like terms: 6n + -2n = 4n
-8 + 4n + -3n2 = -6n

Solving
-8 + 4n + -3n2 = -6n

Solving for variable 'n'.

Reorder the terms:
-8 + 4n + 6n + -3n2 = -6n + 6n

Combine like terms: 4n + 6n = 10n
-8 + 10n + -3n2 = -6n + 6n

Combine like terms: -6n + 6n = 0
-8 + 10n + -3n2 = 0

Factor a trinomial.
(-2 + n)(4 + -3n) = 0


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

Simplifying
-2 + n = 0

Solving
-2 + n = 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 + n = 0 + 2

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

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

Simplifying
n = 2

Subproblem 2
Set the factor '(4 + -3n)' equal to zero and attempt to solve:

Simplifying
4 + -3n = 0

Solving
4 + -3n = 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 + -3n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3n = 0 + -4
-3n = 0 + -4

Combine like terms: 0 + -4 = -4
-3n = -4

Divide each side by '-3'.
n = 1.333333333

Simplifying
n = 1.333333333
Solution
n = {2, 1.333333333}

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