2(5n+3)=8n+2n(n+3)

Solution for 2(5n+3)=8n+2n(n+3) equation:

Simplifying
2(5n + 3) = 8n + 2n(n + 3)

Reorder the terms:
2(3 + 5n) = 8n + 2n(n + 3)
(3 * 2 + 5n * 2) = 8n + 2n(n + 3)
(6 + 10n) = 8n + 2n(n + 3)

Reorder the terms:
6 + 10n = 8n + 2n(3 + n)
6 + 10n = 8n + (3 * 2n + n * 2n)
6 + 10n = 8n + (6n + 2n2)

Combine like terms: 8n + 6n = 14n
6 + 10n = 14n + 2n2

Solving
6 + 10n = 14n + 2n2

Solving for variable 'n'.

Combine like terms: 10n + -14n = -4n
6 + -4n + -2n2 = 14n + 2n2 + -14n + -2n2

Reorder the terms:
6 + -4n + -2n2 = 14n + -14n + 2n2 + -2n2

Combine like terms: 14n + -14n = 0
6 + -4n + -2n2 = 0 + 2n2 + -2n2
6 + -4n + -2n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
6 + -4n + -2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -2n + -1n2) = 0

Factor a trinomial.
2((1 + -1n)(3 + n)) = 0

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

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

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

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

Simplifying
n = 1
Subproblem 2
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

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

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

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

Simplifying
n = -3
Solution
n = {1, -3}