x(1+9x)-9x=1

Solution for x(1+9x)-9x=1 equation:

Simplifying
x(1 + 9x) + -9x = 1
(1 * x + 9x * x) + -9x = 1
(1x + 9x2) + -9x = 1

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

Combine like terms: 1x + -9x = -8x
-8x + 9x2 = 1

Solving
-8x + 9x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + -8x + 9x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -8x + 9x2 = 0

Factor a trinomial.
(-1 + -9x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-1 + -9x)' equal to zero and attempt to solve:

Simplifying
-1 + -9x = 0

Solving
-1 + -9x = 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 + -9x = 0 + 1

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

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

Divide each side by '-9'.
x = -0.1111111111

Simplifying
x = -0.1111111111
Subproblem 2
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
Solution
x = {-0.1111111111, 1}