(x+0.6)(x+1.8)=0

Solution for (x+0.6)(x+1.8)=0 equation:

Simplifying
(x + 0.6)(x + 1.8) = 0

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

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

Multiply (0.6 + x) * (1.8 + x)
(0.6(1.8 + x) + x(1.8 + x)) = 0
((1.8 * 0.6 + x * 0.6) + x(1.8 + x)) = 0
((1.08 + 0.6x) + x(1.8 + x)) = 0
(1.08 + 0.6x + (1.8 * x + x * x)) = 0
(1.08 + 0.6x + (1.8x + x2)) = 0

Combine like terms: 0.6x + 1.8x = 2.4x
(1.08 + 2.4x + x2) = 0

Solving
1.08 + 2.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1.08' to each side of the equation.
1.08 + 2.4x + -1.08 + x2 = 0 + -1.08

Reorder the terms:
1.08 + -1.08 + 2.4x + x2 = 0 + -1.08

Combine like terms: 1.08 + -1.08 = 0.00
0.00 + 2.4x + x2 = 0 + -1.08
2.4x + x2 = 0 + -1.08

Combine like terms: 0 + -1.08 = -1.08
2.4x + x2 = -1.08

The x term is 2.4x.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4x + 1.44 + x2 = -1.08 + 1.44

Reorder the terms:
1.44 + 2.4x + x2 = -1.08 + 1.44

Combine like terms: -1.08 + 1.44 = 0.36
1.44 + 2.4x + x2 = 0.36

Factor a perfect square on the left side:
(x + 1.2)(x + 1.2) = 0.36

Calculate the square root of the right side: 0.6

Break this problem into two subproblems by setting 
(x + 1.2) equal to 0.6 and -0.6.

Subproblem 1
x + 1.2 = 0.6

Simplifying
x + 1.2 = 0.6

Reorder the terms:
1.2 + x = 0.6

Solving
1.2 + x = 0.6

Solving for variable 'x'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + x = 0.6 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + x = 0.6 + -1.2
x = 0.6 + -1.2

Combine like terms: 0.6 + -1.2 = -0.6
x = -0.6

Simplifying
x = -0.6

Subproblem 2
x + 1.2 = -0.6

Simplifying
x + 1.2 = -0.6

Reorder the terms:
1.2 + x = -0.6

Solving
1.2 + x = -0.6

Solving for variable 'x'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + x = -0.6 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + x = -0.6 + -1.2
x = -0.6 + -1.2

Combine like terms: -0.6 + -1.2 = -1.8
x = -1.8

Simplifying
x = -1.8

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.6, -1.8}