(x+0.5)(x+1.2)=0

Solution for (x+0.5)(x+1.2)=0 equation:

Simplifying
(x + 0.5)(x + 1.2) = 0

Reorder the terms:
(0.5 + x)(x + 1.2) = 0

Reorder the terms:
(0.5 + x)(1.2 + x) = 0

Multiply (0.5 + x) * (1.2 + x)
(0.5(1.2 + x) + x(1.2 + x)) = 0
((1.2 * 0.5 + x * 0.5) + x(1.2 + x)) = 0
((0.6 + 0.5x) + x(1.2 + x)) = 0
(0.6 + 0.5x + (1.2 * x + x * x)) = 0
(0.6 + 0.5x + (1.2x + x2)) = 0

Combine like terms: 0.5x + 1.2x = 1.7x
(0.6 + 1.7x + x2) = 0

Solving
0.6 + 1.7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + 1.7x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + 1.7x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + 1.7x + x2 = 0 + -0.6
1.7x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
1.7x + x2 = -0.6

The x term is 1.7x.  Take half its coefficient (0.85).
Square it (0.7225) and add it to both sides.

Add '0.7225' to each side of the equation.
1.7x + 0.7225 + x2 = -0.6 + 0.7225

Reorder the terms:
0.7225 + 1.7x + x2 = -0.6 + 0.7225

Combine like terms: -0.6 + 0.7225 = 0.1225
0.7225 + 1.7x + x2 = 0.1225

Factor a perfect square on the left side:
(x + 0.85)(x + 0.85) = 0.1225

Calculate the square root of the right side: 0.35

Break this problem into two subproblems by setting 
(x + 0.85) equal to 0.35 and -0.35.

Subproblem 1
x + 0.85 = 0.35

Simplifying
x + 0.85 = 0.35

Reorder the terms:
0.85 + x = 0.35

Solving
0.85 + x = 0.35

Solving for variable 'x'.

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

Add '-0.85' to each side of the equation.
0.85 + -0.85 + x = 0.35 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + x = 0.35 + -0.85
x = 0.35 + -0.85

Combine like terms: 0.35 + -0.85 = -0.5
x = -0.5

Simplifying
x = -0.5

Subproblem 2
x + 0.85 = -0.35

Simplifying
x + 0.85 = -0.35

Reorder the terms:
0.85 + x = -0.35

Solving
0.85 + x = -0.35

Solving for variable 'x'.

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

Add '-0.85' to each side of the equation.
0.85 + -0.85 + x = -0.35 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + x = -0.35 + -0.85
x = -0.35 + -0.85

Combine like terms: -0.35 + -0.85 = -1.2
x = -1.2

Simplifying
x = -1.2

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.5, -1.2}