2n^2+14n+5=3n

Solution for 2n^2+14n+5=3n equation:

Simplifying
2n2 + 14n + 5 = 3n

Reorder the terms:
5 + 14n + 2n2 = 3n

Solving
5 + 14n + 2n2 = 3n

Solving for variable 'n'.

Reorder the terms:
5 + 14n + -3n + 2n2 = 3n + -3n

Combine like terms: 14n + -3n = 11n
5 + 11n + 2n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
5 + 11n + 2n2 = 0

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

Subproblem 1
Set the factor '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 0

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

Add '-5' to each side of the equation.
5 + -5 + n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + n = 0 + -5
n = 0 + -5

Combine like terms: 0 + -5 = -5
n = -5

Simplifying
n = -5
Subproblem 2
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
Solution
n = {-5, -0.5}