2n(n^2-4n+10)=

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Solution for 2n(n^2-4n+10)= equation: 


Simplifying
2n(n2 + -4n + 10) = 0

Reorder the terms:
2n(10 + -4n + n2) = 0
(10 * 2n + -4n * 2n + n2 * 2n) = 0
(20n + -8n2 + 2n3) = 0

Solving
20n + -8n2 + 2n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2n'.
2n(10 + -4n + n2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(10 + -4n + n2)' equal to zero and attempt to solve:

Simplifying
10 + -4n + n2 = 0

Solving
10 + -4n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -4n + -10 + n2 = 0 + -10

Reorder the terms:
10 + -10 + -4n + n2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -4n + n2 = 0 + -10
-4n + n2 = 0 + -10

Combine like terms: 0 + -10 = -10
-4n + n2 = -10

The n term is -4n.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4n + 4 + n2 = -10 + 4

Reorder the terms:
4 + -4n + n2 = -10 + 4

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

Factor a perfect square on the left side:
(n + -2)(n + -2) = -6

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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