(1-2x)*(x-3)=2

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

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

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

Multiply (1 + -2x) * (-3 + x)
(1(-3 + x) + -2x * (-3 + x)) = 2
((-3 * 1 + x * 1) + -2x * (-3 + x)) = 2
((-3 + 1x) + -2x * (-3 + x)) = 2
(-3 + 1x + (-3 * -2x + x * -2x)) = 2
(-3 + 1x + (6x + -2x2)) = 2

Combine like terms: 1x + 6x = 7x
(-3 + 7x + -2x2) = 2

Solving
-3 + 7x + -2x2 = 2

Solving for variable 'x'.

Reorder the terms:
-3 + -2 + 7x + -2x2 = 2 + -2

Combine like terms: -3 + -2 = -5
-5 + 7x + -2x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-5 + 7x + -2x2 = 0

Factor a trinomial.
(-5 + 2x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-5 + 2x)' equal to zero and attempt to solve:

Simplifying
-5 + 2x = 0

Solving
-5 + 2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + 2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2x = 0 + 5
2x = 0 + 5

Combine like terms: 0 + 5 = 5
2x = 5

Divide each side by '2'.
x = 2.5

Simplifying
x = 2.5
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 = {2.5, 1}