(-x+1)(-2x+3)=0

Solution for (-x+1)(-2x+3)=0 equation:

Simplifying
(-1x + 1)(-2x + 3) = 0

Reorder the terms:
(1 + -1x)(-2x + 3) = 0

Reorder the terms:
(1 + -1x)(3 + -2x) = 0

Multiply (1 + -1x) * (3 + -2x)
(1(3 + -2x) + -1x * (3 + -2x)) = 0
((3 * 1 + -2x * 1) + -1x * (3 + -2x)) = 0
((3 + -2x) + -1x * (3 + -2x)) = 0
(3 + -2x + (3 * -1x + -2x * -1x)) = 0
(3 + -2x + (-3x + 2x2)) = 0

Combine like terms: -2x + -3x = -5x
(3 + -5x + 2x2) = 0

Solving
3 + -5x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(3 + -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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {1, 1.5}