(x+0.5)(x+1.8)=0

Solution for (x+0.5)(x+1.8)=0 equation:

Simplifying
(x + 0.5)(x + 1.8) = 0

Reorder the terms:
(0.5 + x)(x + 1.8) = 0

Reorder the terms:
(0.5 + x)(1.8 + x) = 0

Multiply (0.5 + x) * (1.8 + x)
(0.5(1.8 + x) + x(1.8 + x)) = 0
((1.8 * 0.5 + x * 0.5) + x(1.8 + x)) = 0
((0.9 + 0.5x) + x(1.8 + x)) = 0
(0.9 + 0.5x + (1.8 * x + x * x)) = 0
(0.9 + 0.5x + (1.8x + x2)) = 0

Combine like terms: 0.5x + 1.8x = 2.3x
(0.9 + 2.3x + x2) = 0

Solving
0.9 + 2.3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.9' to each side of the equation.
0.9 + 2.3x + -0.9 + x2 = 0 + -0.9

Reorder the terms:
0.9 + -0.9 + 2.3x + x2 = 0 + -0.9

Combine like terms: 0.9 + -0.9 = 0.0
0.0 + 2.3x + x2 = 0 + -0.9
2.3x + x2 = 0 + -0.9

Combine like terms: 0 + -0.9 = -0.9
2.3x + x2 = -0.9

The x term is 2.3x.  Take half its coefficient (1.15).
Square it (1.3225) and add it to both sides.

Add '1.3225' to each side of the equation.
2.3x + 1.3225 + x2 = -0.9 + 1.3225

Reorder the terms:
1.3225 + 2.3x + x2 = -0.9 + 1.3225

Combine like terms: -0.9 + 1.3225 = 0.4225
1.3225 + 2.3x + x2 = 0.4225

Factor a perfect square on the left side:
(x + 1.15)(x + 1.15) = 0.4225

Calculate the square root of the right side: 0.65

Break this problem into two subproblems by setting 
(x + 1.15) equal to 0.65 and -0.65.

Subproblem 1
x + 1.15 = 0.65

Simplifying
x + 1.15 = 0.65

Reorder the terms:
1.15 + x = 0.65

Solving
1.15 + x = 0.65

Solving for variable 'x'.

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

Add '-1.15' to each side of the equation.
1.15 + -1.15 + x = 0.65 + -1.15

Combine like terms: 1.15 + -1.15 = 0.00
0.00 + x = 0.65 + -1.15
x = 0.65 + -1.15

Combine like terms: 0.65 + -1.15 = -0.5
x = -0.5

Simplifying
x = -0.5

Subproblem 2
x + 1.15 = -0.65

Simplifying
x + 1.15 = -0.65

Reorder the terms:
1.15 + x = -0.65

Solving
1.15 + x = -0.65

Solving for variable 'x'.

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

Add '-1.15' to each side of the equation.
1.15 + -1.15 + x = -0.65 + -1.15

Combine like terms: 1.15 + -1.15 = 0.00
0.00 + x = -0.65 + -1.15
x = -0.65 + -1.15

Combine like terms: -0.65 + -1.15 = -1.8
x = -1.8

Simplifying
x = -1.8

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.5, -1.8}