7n^2-n+1=7

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

Simplifying
7n2 + -1n + 1 = 7

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

Solving
1 + -1n + 7n2 = 7

Solving for variable 'n'.

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

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

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

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

Subproblem 1
Set the factor '(-6 + -7n)' equal to zero and attempt to solve:

Simplifying
-6 + -7n = 0

Solving
-6 + -7n = 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 + -7n = 0 + 6

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

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

Divide each side by '-7'.
n = -0.8571428571

Simplifying
n = -0.8571428571
Subproblem 2
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
Solution
n = {-0.8571428571, 1}