x^2-2x+1=81x^2

Solution for x^2-2x+1=81x^2 equation:

Simplifying
x2 + -2x + 1 = 81x2

Reorder the terms:
1 + -2x + x2 = 81x2

Solving
1 + -2x + x2 = 81x2

Solving for variable 'x'.

Combine like terms: x2 + -81x2 = -80x2
1 + -2x + -80x2 = 81x2 + -81x2

Combine like terms: 81x2 + -81x2 = 0
1 + -2x + -80x2 = 0

Factor a trinomial.
(1 + -10x)(1 + 8x) = 0

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

Simplifying
1 + -10x = 0

Solving
1 + -10x = 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 + -10x = 0 + -1

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

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

Divide each side by '-10'.
x = 0.1

Simplifying
x = 0.1
Subproblem 2
Set the factor '(1 + 8x)' equal to zero and attempt to solve:

Simplifying
1 + 8x = 0

Solving
1 + 8x = 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 + 8x = 0 + -1

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

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

Divide each side by '8'.
x = -0.125

Simplifying
x = -0.125
Solution
x = {0.1, -0.125}