2=n(2n+3)

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

Simplifying
2 = n(2n + 3)

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

Solving
2 = 3n + 2n2

Solving for variable 'n'.

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

Combine like terms: 3n + -3n = 0
2 + -3n + -2n2 = 0 + 2n2 + -2n2
2 + -3n + -2n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
2 + -3n + -2n2 = 0

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

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

Simplifying
1 + -2n = 0

Solving
1 + -2n = 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 + -2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2n = 0 + -1
-2n = 0 + -1

Combine like terms: 0 + -1 = -1
-2n = -1

Divide each side by '-2'.
n = 0.5

Simplifying
n = 0.5
Subproblem 2
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
Solution
n = {0.5, -2}