(2x-3)(2x-1.5)=

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Solution for (2x-3)(2x-1.5)= equation: 


Simplifying
(2x + -3)(2x + -1.5) = 0

Reorder the terms:
(-3 + 2x)(2x + -1.5) = 0

Reorder the terms:
(-3 + 2x)(-1.5 + 2x) = 0

Multiply (-3 + 2x) * (-1.5 + 2x)
(-3(-1.5 + 2x) + 2x * (-1.5 + 2x)) = 0
((-1.5 * -3 + 2x * -3) + 2x * (-1.5 + 2x)) = 0
((4.5 + -6x) + 2x * (-1.5 + 2x)) = 0
(4.5 + -6x + (-1.5 * 2x + 2x * 2x)) = 0
(4.5 + -6x + (-3x + 4x2)) = 0

Combine like terms: -6x + -3x = -9x
(4.5 + -9x + 4x2) = 0

Solving
4.5 + -9x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
1.125 + -2.25x + x2 = 0

Move the constant term to the right:

Add '-1.125' to each side of the equation.
1.125 + -2.25x + -1.125 + x2 = 0 + -1.125

Reorder the terms:
1.125 + -1.125 + -2.25x + x2 = 0 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + -2.25x + x2 = 0 + -1.125
-2.25x + x2 = 0 + -1.125

Combine like terms: 0 + -1.125 = -1.125
-2.25x + x2 = -1.125

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 = -1.125 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = -1.125 + 1.265625

Combine like terms: -1.125 + 1.265625 = 0.140625
1.265625 + -2.25x + x2 = 0.140625

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 0.140625

Calculate the square root of the right side: 0.375

Break this problem into two subproblems by setting 
(x + -1.125) equal to 0.375 and -0.375.


Subproblem 1
x + -1.125 = 0.375

Simplifying
x + -1.125 = 0.375

Reorder the terms:
-1.125 + x = 0.375

Solving
-1.125 + x = 0.375

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 = 0.375 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = 0.375 + 1.125
x = 0.375 + 1.125

Combine like terms: 0.375 + 1.125 = 1.5
x = 1.5

Simplifying
x = 1.5


Subproblem 2
x + -1.125 = -0.375

Simplifying
x + -1.125 = -0.375

Reorder the terms:
-1.125 + x = -0.375

Solving
-1.125 + x = -0.375

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 = -0.375 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + x = -0.375 + 1.125
x = -0.375 + 1.125

Combine like terms: -0.375 + 1.125 = 0.75
x = 0.75

Simplifying
x = 0.75


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5, 0.75}

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