10-1X=10X-1X^2

Solution for 10-1X=10X-1X^2 equation:

Simplifying
10 + -1X = 10X + -1X2

Solving
10 + -1X = 10X + -1X2

Solving for variable 'X'.

Combine like terms: -1X + -10X = -11X
10 + -11X + X2 = 10X + -1X2 + -10X + X2

Reorder the terms:
10 + -11X + X2 = 10X + -10X + -1X2 + X2

Combine like terms: 10X + -10X = 0
10 + -11X + X2 = 0 + -1X2 + X2
10 + -11X + X2 = -1X2 + X2

Combine like terms: -1X2 + X2 = 0
10 + -11X + 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}