(n-1)(7n+2)=90

Solution for (n-1)(7n+2)=90 equation:

Simplifying
(n + -1)(7n + 2) = 90

Reorder the terms:
(-1 + n)(7n + 2) = 90

Reorder the terms:
(-1 + n)(2 + 7n) = 90

Multiply (-1 + n) * (2 + 7n)
(-1(2 + 7n) + n(2 + 7n)) = 90
((2 * -1 + 7n * -1) + n(2 + 7n)) = 90
((-2 + -7n) + n(2 + 7n)) = 90
(-2 + -7n + (2 * n + 7n * n)) = 90
(-2 + -7n + (2n + 7n2)) = 90

Combine like terms: -7n + 2n = -5n
(-2 + -5n + 7n2) = 90

Solving
-2 + -5n + 7n2 = 90

Solving for variable 'n'.

Reorder the terms:
-2 + -90 + -5n + 7n2 = 90 + -90

Combine like terms: -2 + -90 = -92
-92 + -5n + 7n2 = 90 + -90

Combine like terms: 90 + -90 = 0
-92 + -5n + 7n2 = 0

Factor a trinomial.
(-23 + -7n)(4 + -1n) = 0

Subproblem 1
Set the factor '(-23 + -7n)' equal to zero and attempt to solve:

Simplifying
-23 + -7n = 0

Solving
-23 + -7n = 0

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

Add '23' to each side of the equation.
-23 + 23 + -7n = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -7n = 0 + 23
-7n = 0 + 23

Combine like terms: 0 + 23 = 23
-7n = 23

Divide each side by '-7'.
n = -3.285714286

Simplifying
n = -3.285714286
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-3.285714286, 4}