n(7n+28)=224

Solution for n(7n+28)=224 equation:

Simplifying
n(7n + 28) = 224

Reorder the terms:
n(28 + 7n) = 224
(28 * n + 7n * n) = 224
(28n + 7n2) = 224

Solving
28n + 7n2 = 224

Solving for variable 'n'.

Reorder the terms:
-224 + 28n + 7n2 = 224 + -224

Combine like terms: 224 + -224 = 0
-224 + 28n + 7n2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-32 + 4n + n2) = 0

Factor a trinomial.
7((-8 + -1n)(4 + -1n)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve:

Simplifying
-8 + -1n = 0

Solving
-8 + -1n = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1n = 0 + 8
-1n = 0 + 8

Combine like terms: 0 + 8 = 8
-1n = 8

Divide each side by '-1'.
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-8, 4}