7n^2-48=34n

Solution for 7n^2-48=34n equation:

Simplifying
7n2 + -48 = 34n

Reorder the terms:
-48 + 7n2 = 34n

Solving
-48 + 7n2 = 34n

Solving for variable 'n'.

Reorder the terms:
-48 + -34n + 7n2 = 34n + -34n

Combine like terms: 34n + -34n = 0
-48 + -34n + 7n2 = 0

Factor a trinomial.
(-8 + -7n)(6 + -1n) = 0

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

Simplifying
-8 + -7n = 0

Solving
-8 + -7n = 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 + -7n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -7n = 0 + 8
-7n = 0 + 8

Combine like terms: 0 + 8 = 8
-7n = 8

Divide each side by '-7'.
n = -1.142857143

Simplifying
n = -1.142857143
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-1.142857143, 6}