3n(n+10)=8n

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Solution for 3n(n+10)=8n equation: 


Simplifying
3n(n + 10) = 8n

Reorder the terms:
3n(10 + n) = 8n
(10 * 3n + n * 3n) = 8n
(30n + 3n2) = 8n

Solving
30n + 3n2 = 8n

Solving for variable 'n'.

Reorder the terms:
30n + -8n + 3n2 = 8n + -8n

Combine like terms: 30n + -8n = 22n
22n + 3n2 = 8n + -8n

Combine like terms: 8n + -8n = 0
22n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(22 + 3n) = 0


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 '(22 + 3n)' equal to zero and attempt to solve:

Simplifying
22 + 3n = 0

Solving
22 + 3n = 0

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

Add '-22' to each side of the equation.
22 + -22 + 3n = 0 + -22

Combine like terms: 22 + -22 = 0
0 + 3n = 0 + -22
3n = 0 + -22

Combine like terms: 0 + -22 = -22
3n = -22

Divide each side by '3'.
n = -7.333333333

Simplifying
n = -7.333333333
Solution
n = {0, -7.333333333}

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