20=0.5(x+3)(2x-5)

Solution for 20=0.5(x+3)(2x-5) equation:

Simplifying
20 = 0.5(x + 3)(2x + -5)

Reorder the terms:
20 = 0.5(3 + x)(2x + -5)

Reorder the terms:
20 = 0.5(3 + x)(-5 + 2x)

Multiply (3 + x) * (-5 + 2x)
20 = 0.5(3(-5 + 2x) + x(-5 + 2x))
20 = 0.5((-5 * 3 + 2x * 3) + x(-5 + 2x))
20 = 0.5((-15 + 6x) + x(-5 + 2x))
20 = 0.5(-15 + 6x + (-5 * x + 2x * x))
20 = 0.5(-15 + 6x + (-5x + 2x2))

Combine like terms: 6x + -5x = 1x
20 = 0.5(-15 + 1x + 2x2)
20 = (-15 * 0.5 + 1x * 0.5 + 2x2 * 0.5)
20 = (-7.5 + 0.5x + 1x2)

Solving
20 = -7.5 + 0.5x + 1x2

Solving for variable 'x'.

Combine like terms: 20 + 7.5 = 27.5
27.5 + -0.5x + -1x2 = -7.5 + 0.5x + 1x2 + 7.5 + -0.5x + -1x2

Reorder the terms:
27.5 + -0.5x + -1x2 = -7.5 + 7.5 + 0.5x + -0.5x + 1x2 + -1x2

Combine like terms: -7.5 + 7.5 = 0.0
27.5 + -0.5x + -1x2 = 0.0 + 0.5x + -0.5x + 1x2 + -1x2
27.5 + -0.5x + -1x2 = 0.5x + -0.5x + 1x2 + -1x2

Combine like terms: 0.5x + -0.5x = 0.0
27.5 + -0.5x + -1x2 = 0.0 + 1x2 + -1x2
27.5 + -0.5x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
27.5 + -0.5x + -1x2 = 0

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

Divide each side by '-1'.
-27.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '27.5' to each side of the equation.
-27.5 + 0.5x + 27.5 + x2 = 0 + 27.5

Reorder the terms:
-27.5 + 27.5 + 0.5x + x2 = 0 + 27.5

Combine like terms: -27.5 + 27.5 = 0.0
0.0 + 0.5x + x2 = 0 + 27.5
0.5x + x2 = 0 + 27.5

Combine like terms: 0 + 27.5 = 27.5
0.5x + x2 = 27.5

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 = 27.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 27.5 + 0.0625

Combine like terms: 27.5 + 0.0625 = 27.5625
0.0625 + 0.5x + x2 = 27.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 27.5625

Calculate the square root of the right side: 5.25

Break this problem into two subproblems by setting 
(x + 0.25) equal to 5.25 and -5.25.

Subproblem 1
x + 0.25 = 5.25

Simplifying
x + 0.25 = 5.25

Reorder the terms:
0.25 + x = 5.25

Solving
0.25 + x = 5.25

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 = 5.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 5.25 + -0.25
x = 5.25 + -0.25

Combine like terms: 5.25 + -0.25 = 5
x = 5

Simplifying
x = 5

Subproblem 2
x + 0.25 = -5.25

Simplifying
x + 0.25 = -5.25

Reorder the terms:
0.25 + x = -5.25

Solving
0.25 + x = -5.25

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 = -5.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -5.25 + -0.25
x = -5.25 + -0.25

Combine like terms: -5.25 + -0.25 = -5.5
x = -5.5

Simplifying
x = -5.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5, -5.5}