x^2-9=9x+1

Solution for x^2-9=9x+1 equation:

Simplifying
x2 + -9 = 9x + 1

Reorder the terms:
-9 + x2 = 9x + 1

Reorder the terms:
-9 + x2 = 1 + 9x

Solving
-9 + x2 = 1 + 9x

Solving for variable 'x'.

Reorder the terms:
-9 + -1 + -9x + x2 = 1 + 9x + -1 + -9x

Combine like terms: -9 + -1 = -10
-10 + -9x + x2 = 1 + 9x + -1 + -9x

Reorder the terms:
-10 + -9x + x2 = 1 + -1 + 9x + -9x

Combine like terms: 1 + -1 = 0
-10 + -9x + x2 = 0 + 9x + -9x
-10 + -9x + x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-10 + -9x + x2 = 0

Factor a trinomial.
(-1 + -1x)(10 + -1x) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-1, 10}