1+2x-(1+2x)x=0

Solution for 1+2x-(1+2x)x=0 equation:

Simplifying
1 + 2x + -1(1 + 2x) * x = 0

Reorder the terms for easier multiplication:
1 + 2x + -1x(1 + 2x) = 0
1 + 2x + (1 * -1x + 2x * -1x) = 0
1 + 2x + (-1x + -2x2) = 0

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

Solving
1 + 1x + -2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(1 + 2x) = 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 '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {1, -0.5}