176=2n^2+21n

Solution for 176=2n^2+21n equation:

Simplifying
176 = 2n2 + 21n

Reorder the terms:
176 = 21n + 2n2

Solving
176 = 21n + 2n2

Solving for variable 'n'.

Reorder the terms:
176 + -21n + -2n2 = 21n + -21n + 2n2 + -2n2

Combine like terms: 21n + -21n = 0
176 + -21n + -2n2 = 0 + 2n2 + -2n2
176 + -21n + -2n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
176 + -21n + -2n2 = 0

Factor a trinomial.
(11 + -2n)(16 + n) = 0

Subproblem 1
Set the factor '(11 + -2n)' equal to zero and attempt to solve:

Simplifying
11 + -2n = 0

Solving
11 + -2n = 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 + -2n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2n = 0 + -11
-2n = 0 + -11

Combine like terms: 0 + -11 = -11
-2n = -11

Divide each side by '-2'.
n = 5.5

Simplifying
n = 5.5
Subproblem 2
Set the factor '(16 + n)' equal to zero and attempt to solve:

Simplifying
16 + n = 0

Solving
16 + n = 0

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

Add '-16' to each side of the equation.
16 + -16 + n = 0 + -16

Combine like terms: 16 + -16 = 0
0 + n = 0 + -16
n = 0 + -16

Combine like terms: 0 + -16 = -16
n = -16

Simplifying
n = -16
Solution
n = {5.5, -16}