(x+0.8)(x+1.5)=0

Solution for (x+0.8)(x+1.5)=0 equation:

Simplifying
(x + 0.8)(x + 1.5) = 0

Reorder the terms:
(0.8 + x)(x + 1.5) = 0

Reorder the terms:
(0.8 + x)(1.5 + x) = 0

Multiply (0.8 + x) * (1.5 + x)
(0.8(1.5 + x) + x(1.5 + x)) = 0
((1.5 * 0.8 + x * 0.8) + x(1.5 + x)) = 0
((1.2 + 0.8x) + x(1.5 + x)) = 0
(1.2 + 0.8x + (1.5 * x + x * x)) = 0
(1.2 + 0.8x + (1.5x + x2)) = 0

Combine like terms: 0.8x + 1.5x = 2.3x
(1.2 + 2.3x + x2) = 0

Solving
1.2 + 2.3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + 2.3x + -1.2 + x2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + 2.3x + x2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 2.3x + x2 = 0 + -1.2
2.3x + x2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
2.3x + x2 = -1.2

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 = -1.2 + 1.3225

Reorder the terms:
1.3225 + 2.3x + x2 = -1.2 + 1.3225

Combine like terms: -1.2 + 1.3225 = 0.1225
1.3225 + 2.3x + x2 = 0.1225

Factor a perfect square on the left side:
(x + 1.15)(x + 1.15) = 0.1225

Calculate the square root of the right side: 0.35

Break this problem into two subproblems by setting 
(x + 1.15) equal to 0.35 and -0.35.

Subproblem 1
x + 1.15 = 0.35

Simplifying
x + 1.15 = 0.35

Reorder the terms:
1.15 + x = 0.35

Solving
1.15 + x = 0.35

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 = 0.35 + -1.15

Combine like terms: 1.15 + -1.15 = 0.00
0.00 + x = 0.35 + -1.15
x = 0.35 + -1.15

Combine like terms: 0.35 + -1.15 = -0.8
x = -0.8

Simplifying
x = -0.8

Subproblem 2
x + 1.15 = -0.35

Simplifying
x + 1.15 = -0.35

Reorder the terms:
1.15 + x = -0.35

Solving
1.15 + x = -0.35

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 = -0.35 + -1.15

Combine like terms: 1.15 + -1.15 = 0.00
0.00 + x = -0.35 + -1.15
x = -0.35 + -1.15

Combine like terms: -0.35 + -1.15 = -1.5
x = -1.5

Simplifying
x = -1.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.8, -1.5}