7n^2+112=56n

Solution for 7n^2+112=56n equation:

Simplifying
7n2 + 112 = 56n

Reorder the terms:
112 + 7n2 = 56n

Solving
112 + 7n2 = 56n

Solving for variable 'n'.

Reorder the terms:
112 + -56n + 7n2 = 56n + -56n

Combine like terms: 56n + -56n = 0
112 + -56n + 7n2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(16 + -8n + n2) = 0

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

Ignore the factor 7.
Subproblem 1
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
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 = {4, 4}