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

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

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

Reorder the terms:
(-2 + x)(-1x + 1) = 0

Reorder the terms:
(-2 + x)(1 + -1x) = 0

Multiply (-2 + x) * (1 + -1x)
(-2(1 + -1x) + x(1 + -1x)) = 0
((1 * -2 + -1x * -2) + x(1 + -1x)) = 0
((-2 + 2x) + x(1 + -1x)) = 0
(-2 + 2x + (1 * x + -1x * x)) = 0
(-2 + 2x + (1x + -1x2)) = 0

Combine like terms: 2x + 1x = 3x
(-2 + 3x + -1x2) = 0

Solving
-2 + 3x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2 + x)(1 + -1x) = 0

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

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

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

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

Simplifying
x = 2
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 = {2, 1}