3n^2+8n-1=10

Solution for 3n^2+8n-1=10 equation:

Simplifying
3n2 + 8n + -1 = 10

Reorder the terms:
-1 + 8n + 3n2 = 10

Solving
-1 + 8n + 3n2 = 10

Solving for variable 'n'.

Reorder the terms:
-1 + -10 + 8n + 3n2 = 10 + -10

Combine like terms: -1 + -10 = -11
-11 + 8n + 3n2 = 10 + -10

Combine like terms: 10 + -10 = 0
-11 + 8n + 3n2 = 0

Factor a trinomial.
(-11 + -3n)(1 + -1n) = 0

Subproblem 1
Set the factor '(-11 + -3n)' equal to zero and attempt to solve:

Simplifying
-11 + -3n = 0

Solving
-11 + -3n = 0

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

Add '11' to each side of the equation.
-11 + 11 + -3n = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3n = 0 + 11
-3n = 0 + 11

Combine like terms: 0 + 11 = 11
-3n = 11

Divide each side by '-3'.
n = -3.666666667

Simplifying
n = -3.666666667
Subproblem 2
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
Solution
n = {-3.666666667, 1}