44=(x+2)(2x-3)

Solution for 44=(x+2)(2x-3) equation:

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

Reorder the terms:
44 = (2 + x)(2x + -3)

Reorder the terms:
44 = (2 + x)(-3 + 2x)

Multiply (2 + x) * (-3 + 2x)
44 = (2(-3 + 2x) + x(-3 + 2x))
44 = ((-3 * 2 + 2x * 2) + x(-3 + 2x))
44 = ((-6 + 4x) + x(-3 + 2x))
44 = (-6 + 4x + (-3 * x + 2x * x))
44 = (-6 + 4x + (-3x + 2x2))

Combine like terms: 4x + -3x = 1x
44 = (-6 + 1x + 2x2)

Solving
44 = -6 + 1x + 2x2

Solving for variable 'x'.

Combine like terms: 44 + 6 = 50
50 + -1x + -2x2 = -6 + 1x + 2x2 + 6 + -1x + -2x2

Reorder the terms:
50 + -1x + -2x2 = -6 + 6 + 1x + -1x + 2x2 + -2x2

Combine like terms: -6 + 6 = 0
50 + -1x + -2x2 = 0 + 1x + -1x + 2x2 + -2x2
50 + -1x + -2x2 = 1x + -1x + 2x2 + -2x2

Combine like terms: 1x + -1x = 0
50 + -1x + -2x2 = 0 + 2x2 + -2x2
50 + -1x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
50 + -1x + -2x2 = 0

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

Divide each side by '-2'.
-25 + 0.5x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 0.5x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + 0.5x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 0.5x + x2 = 0 + 25
0.5x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
0.5x + x2 = 25

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 25 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 25 + 0.0625

Combine like terms: 25 + 0.0625 = 25.0625
0.0625 + 0.5x + x2 = 25.0625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 25.0625

Calculate the square root of the right side: 5.006246099

Break this problem into two subproblems by setting 
(x + 0.25) equal to 5.006246099 and -5.006246099.

Subproblem 1
x + 0.25 = 5.006246099

Simplifying
x + 0.25 = 5.006246099

Reorder the terms:
0.25 + x = 5.006246099

Solving
0.25 + x = 5.006246099

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 5.006246099 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 5.006246099 + -0.25
x = 5.006246099 + -0.25

Combine like terms: 5.006246099 + -0.25 = 4.756246099
x = 4.756246099

Simplifying
x = 4.756246099

Subproblem 2
x + 0.25 = -5.006246099

Simplifying
x + 0.25 = -5.006246099

Reorder the terms:
0.25 + x = -5.006246099

Solving
0.25 + x = -5.006246099

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -5.006246099 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -5.006246099 + -0.25
x = -5.006246099 + -0.25

Combine like terms: -5.006246099 + -0.25 = -5.256246099
x = -5.256246099

Simplifying
x = -5.256246099

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.756246099, -5.256246099}