(x+4)(x-0.5)=0h

Solution for (x+4)(x-0.5)=0h equation:

Simplifying
(x + 4)(x + -0.5) = 0h

Reorder the terms:
(4 + x)(x + -0.5) = 0h

Reorder the terms:
(4 + x)(-0.5 + x) = 0h

Multiply (4 + x) * (-0.5 + x)
(4(-0.5 + x) + x(-0.5 + x)) = 0h
((-0.5 * 4 + x * 4) + x(-0.5 + x)) = 0h
((-2 + 4x) + x(-0.5 + x)) = 0h
(-2 + 4x + (-0.5 * x + x * x)) = 0h
(-2 + 4x + (-0.5x + x2)) = 0h

Combine like terms: 4x + -0.5x = 3.5x
(-2 + 3.5x + x2) = 0h

Anything times zero is zero.
-2 + 3.5x + x2 = 0h

Solving
-2 + 3.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 3.5x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 3.5x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3.5x + x2 = 0 + 2
3.5x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
3.5x + x2 = 2

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 2 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 2 + 3.0625

Combine like terms: 2 + 3.0625 = 5.0625
3.0625 + 3.5x + x2 = 5.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 5.0625

Calculate the square root of the right side: 2.25

Break this problem into two subproblems by setting 
(x + 1.75) equal to 2.25 and -2.25.

Subproblem 1
x + 1.75 = 2.25

Simplifying
x + 1.75 = 2.25

Reorder the terms:
1.75 + x = 2.25

Solving
1.75 + x = 2.25

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 2.25 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 2.25 + -1.75
x = 2.25 + -1.75

Combine like terms: 2.25 + -1.75 = 0.5
x = 0.5

Simplifying
x = 0.5

Subproblem 2
x + 1.75 = -2.25

Simplifying
x + 1.75 = -2.25

Reorder the terms:
1.75 + x = -2.25

Solving
1.75 + x = -2.25

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -2.25 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -2.25 + -1.75
x = -2.25 + -1.75

Combine like terms: -2.25 + -1.75 = -4
x = -4

Simplifying
x = -4

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, -4}