7n^2+48n-5=7n+1

Solution for 7n^2+48n-5=7n+1 equation:

Simplifying
7n2 + 48n + -5 = 7n + 1

Reorder the terms:
-5 + 48n + 7n2 = 7n + 1

Reorder the terms:
-5 + 48n + 7n2 = 1 + 7n

Solving
-5 + 48n + 7n2 = 1 + 7n

Solving for variable 'n'.

Reorder the terms:
-5 + -1 + 48n + -7n + 7n2 = 1 + 7n + -1 + -7n

Combine like terms: -5 + -1 = -6
-6 + 48n + -7n + 7n2 = 1 + 7n + -1 + -7n

Combine like terms: 48n + -7n = 41n
-6 + 41n + 7n2 = 1 + 7n + -1 + -7n

Reorder the terms:
-6 + 41n + 7n2 = 1 + -1 + 7n + -7n

Combine like terms: 1 + -1 = 0
-6 + 41n + 7n2 = 0 + 7n + -7n
-6 + 41n + 7n2 = 7n + -7n

Combine like terms: 7n + -7n = 0
-6 + 41n + 7n2 = 0

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

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

Simplifying
1 + -7n = 0

Solving
1 + -7n = 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 + -7n = 0 + -1

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

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

Divide each side by '-7'.
n = 0.1428571429

Simplifying
n = 0.1428571429
Solution
n = {-6, 0.1428571429}