x^2-1+10x-5=90

Solution for x^2-1+10x-5=90 equation:

Simplifying
x2 + -1 + 10x + -5 = 90

Reorder the terms:
-1 + -5 + 10x + x2 = 90

Combine like terms: -1 + -5 = -6
-6 + 10x + x2 = 90

Solving
-6 + 10x + x2 = 90

Solving for variable 'x'.

Reorder the terms:
-6 + -90 + 10x + x2 = 90 + -90

Combine like terms: -6 + -90 = -96
-96 + 10x + x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-96 + 10x + x2 = 0

Factor a trinomial.
(-16 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve:

Simplifying
-16 + -1x = 0

Solving
-16 + -1x = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1x = 0 + 16
-1x = 0 + 16

Combine like terms: 0 + 16 = 16
-1x = 16

Divide each side by '-1'.
x = -16

Simplifying
x = -16
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

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

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

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

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

Simplifying
x = 6
Solution
x = {-16, 6}