7n^2+53n-23=1

Solution for 7n^2+53n-23=1 equation:

Simplifying
7n2 + 53n + -23 = 1

Reorder the terms:
-23 + 53n + 7n2 = 1

Solving
-23 + 53n + 7n2 = 1

Solving for variable 'n'.

Reorder the terms:
-23 + -1 + 53n + 7n2 = 1 + -1

Combine like terms: -23 + -1 = -24
-24 + 53n + 7n2 = 1 + -1

Combine like terms: 1 + -1 = 0
-24 + 53n + 7n2 = 0

Factor a trinomial.
(-8 + -1n)(3 + -7n) = 0

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 '(3 + -7n)' equal to zero and attempt to solve:

Simplifying
3 + -7n = 0

Solving
3 + -7n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -7n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7n = 0 + -3
-7n = 0 + -3

Combine like terms: 0 + -3 = -3
-7n = -3

Divide each side by '-7'.
n = 0.4285714286

Simplifying
n = 0.4285714286
Solution
n = {-8, 0.4285714286}