4n^2+72n+68=

Solution for 4n^2+72n+68= equation:

Simplifying
4n2 + 72n + 68 = 0

Reorder the terms:
68 + 72n + 4n2 = 0

Solving
68 + 72n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(17 + 18n + n2) = 0

Factor a trinomial.
4((17 + n)(1 + n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(17 + n)' equal to zero and attempt to solve:

Simplifying
17 + n = 0

Solving
17 + n = 0

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

Add '-17' to each side of the equation.
17 + -17 + n = 0 + -17

Combine like terms: 17 + -17 = 0
0 + n = 0 + -17
n = 0 + -17

Combine like terms: 0 + -17 = -17
n = -17

Simplifying
n = -17
Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

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

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

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

Simplifying
n = -1
Solution
n = {-17, -1}