(1.5-x)(1.5-2x)=1.5

Solution for (1.5-x)(1.5-2x)=1.5 equation:

Simplifying
(1.5 + -1x)(1.5 + -2x) = 1.5

Multiply (1.5 + -1x) * (1.5 + -2x)
(1.5(1.5 + -2x) + -1x * (1.5 + -2x)) = 1.5
((1.5 * 1.5 + -2x * 1.5) + -1x * (1.5 + -2x)) = 1.5
((2.25 + -3x) + -1x * (1.5 + -2x)) = 1.5
(2.25 + -3x + (1.5 * -1x + -2x * -1x)) = 1.5
(2.25 + -3x + (-1.5x + 2x2)) = 1.5

Combine like terms: -3x + -1.5x = -4.5x
(2.25 + -4.5x + 2x2) = 1.5

Solving
2.25 + -4.5x + 2x2 = 1.5

Solving for variable 'x'.

Reorder the terms:
2.25 + -1.5 + -4.5x + 2x2 = 1.5 + -1.5

Combine like terms: 2.25 + -1.5 = 0.75
0.75 + -4.5x + 2x2 = 1.5 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.75 + -4.5x + 2x2 = 0.0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
0.375 + -2.25x + x2 = 0.0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + -2.25x + -0.375 + x2 = 0.0 + -0.375

Reorder the terms:
0.375 + -0.375 + -2.25x + x2 = 0.0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + -2.25x + x2 = 0.0 + -0.375
-2.25x + x2 = 0.0 + -0.375

Combine like terms: 0.0 + -0.375 = -0.375
-2.25x + x2 = -0.375

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = -0.375 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = -0.375 + 1.265625

Combine like terms: -0.375 + 1.265625 = 0.890625
1.265625 + -2.25x + x2 = 0.890625

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 0.890625

Calculate the square root of the right side: 0.943729304

Break this problem into two subproblems by setting 
(x + -1.125) equal to 0.943729304 and -0.943729304.

Subproblem 1
x + -1.125 = 0.943729304

Simplifying
x + -1.125 = 0.943729304

Reorder the terms:
-1.125 + x = 0.943729304

Solving
-1.125 + x = 0.943729304

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = 0.943729304 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = 0.943729304 + 1.125
x = 0.943729304 + 1.125

Combine like terms: 0.943729304 + 1.125 = 2.068729304
x = 2.068729304

Simplifying
x = 2.068729304

Subproblem 2
x + -1.125 = -0.943729304

Simplifying
x + -1.125 = -0.943729304

Reorder the terms:
-1.125 + x = -0.943729304

Solving
-1.125 + x = -0.943729304

Solving for variable 'x'.

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

Add '1.125' to each side of the equation.
-1.125 + 1.125 + x = -0.943729304 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = -0.943729304 + 1.125
x = -0.943729304 + 1.125

Combine like terms: -0.943729304 + 1.125 = 0.181270696
x = 0.181270696

Simplifying
x = 0.181270696

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.068729304, 0.181270696}