7n^2+49=56n

Solution for 7n^2+49=56n equation:

Simplifying
7n2 + 49 = 56n

Reorder the terms:
49 + 7n2 = 56n

Solving
49 + 7n2 = 56n

Solving for variable 'n'.

Reorder the terms:
49 + -56n + 7n2 = 56n + -56n

Combine like terms: 56n + -56n = 0
49 + -56n + 7n2 = 0

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

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

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

Simplifying
1 + -1n = 0

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

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

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

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

Simplifying
n = 1
Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {1, 7}