240=4n^2+28n

Solution for 240=4n^2+28n equation:

Simplifying
240 = 4n2 + 28n

Reorder the terms:
240 = 28n + 4n2

Solving
240 = 28n + 4n2

Solving for variable 'n'.

Reorder the terms:
240 + -28n + -4n2 = 28n + -28n + 4n2 + -4n2

Combine like terms: 28n + -28n = 0
240 + -28n + -4n2 = 0 + 4n2 + -4n2
240 + -28n + -4n2 = 4n2 + -4n2

Combine like terms: 4n2 + -4n2 = 0
240 + -28n + -4n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(60 + -7n + -1n2) = 0

Factor a trinomial.
4((5 + -1n)(12 + n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 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 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Subproblem 2
Set the factor '(12 + n)' equal to zero and attempt to solve:

Simplifying
12 + n = 0

Solving
12 + n = 0

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

Add '-12' to each side of the equation.
12 + -12 + n = 0 + -12

Combine like terms: 12 + -12 = 0
0 + n = 0 + -12
n = 0 + -12

Combine like terms: 0 + -12 = -12
n = -12

Simplifying
n = -12
Solution
n = {5, -12}