3n^2=8n+3

Solution for 3n^2=8n+3 equation:

Simplifying
3n2 = 8n + 3

Reorder the terms:
3n2 = 3 + 8n

Solving
3n2 = 3 + 8n

Solving for variable 'n'.

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

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

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

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

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

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

Simplifying
-1 + -3n = 0

Solving
-1 + -3n = 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 + -3n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3n = 0 + 1
-3n = 0 + 1

Combine like terms: 0 + 1 = 1
-3n = 1

Divide each side by '-3'.
n = -0.3333333333

Simplifying
n = -0.3333333333
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 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 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-0.3333333333, 3}