x*2.5-x=(1-x)(1.5-x)

Solution for x*2.5-x=(1-x)(1.5-x) equation:

Simplifying
x * 2.5 + -1x = (1 + -1x)(1.5 + -1x)

Reorder the terms for easier multiplication:
2.5x + -1x = (1 + -1x)(1.5 + -1x)

Combine like terms: 2.5x + -1x = 1.5x
1.5x = (1 + -1x)(1.5 + -1x)

Multiply (1 + -1x) * (1.5 + -1x)
1.5x = (1(1.5 + -1x) + -1x * (1.5 + -1x))
1.5x = ((1.5 * 1 + -1x * 1) + -1x * (1.5 + -1x))
1.5x = ((1.5 + -1x) + -1x * (1.5 + -1x))
1.5x = (1.5 + -1x + (1.5 * -1x + -1x * -1x))
1.5x = (1.5 + -1x + (-1.5x + 1x2))

Combine like terms: -1x + -1.5x = -2.5x
1.5x = (1.5 + -2.5x + 1x2)

Solving
1.5x = 1.5 + -2.5x + 1x2

Solving for variable 'x'.

Reorder the terms:
-1.5 + 1.5x + 2.5x + -1x2 = 1.5 + -2.5x + 1x2 + -1.5 + 2.5x + -1x2

Combine like terms: 1.5x + 2.5x = 4x
-1.5 + 4x + -1x2 = 1.5 + -2.5x + 1x2 + -1.5 + 2.5x + -1x2

Reorder the terms:
-1.5 + 4x + -1x2 = 1.5 + -1.5 + -2.5x + 2.5x + 1x2 + -1x2

Combine like terms: 1.5 + -1.5 = 0.0
-1.5 + 4x + -1x2 = 0.0 + -2.5x + 2.5x + 1x2 + -1x2
-1.5 + 4x + -1x2 = -2.5x + 2.5x + 1x2 + -1x2

Combine like terms: -2.5x + 2.5x = 0.0
-1.5 + 4x + -1x2 = 0.0 + 1x2 + -1x2
-1.5 + 4x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-1.5 + 4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1.5 + -4x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -4x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -4x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -4x + x2 = 0 + -1.5
-4x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-4x + x2 = -1.5

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -1.5 + 4

Reorder the terms:
4 + -4x + x2 = -1.5 + 4

Combine like terms: -1.5 + 4 = 2.5
4 + -4x + x2 = 2.5

Factor a perfect square on the left side:
(x + -2)(x + -2) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(x + -2) equal to 1.58113883 and -1.58113883.

Subproblem 1
x + -2 = 1.58113883

Simplifying
x + -2 = 1.58113883

Reorder the terms:
-2 + x = 1.58113883

Solving
-2 + x = 1.58113883

Solving for variable 'x'.

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 = 1.58113883 + 2

Combine like terms: -2 + 2 = 0
0 + x = 1.58113883 + 2
x = 1.58113883 + 2

Combine like terms: 1.58113883 + 2 = 3.58113883
x = 3.58113883

Simplifying
x = 3.58113883

Subproblem 2
x + -2 = -1.58113883

Simplifying
x + -2 = -1.58113883

Reorder the terms:
-2 + x = -1.58113883

Solving
-2 + x = -1.58113883

Solving for variable 'x'.

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 = -1.58113883 + 2

Combine like terms: -2 + 2 = 0
0 + x = -1.58113883 + 2
x = -1.58113883 + 2

Combine like terms: -1.58113883 + 2 = 0.41886117
x = 0.41886117

Simplifying
x = 0.41886117

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.58113883, 0.41886117}