(x+.4)(x+3.2)=0

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Solution for (x+.4)(x+3.2)=0 equation: 


Simplifying
(x + 0.4)(x + 3.2) = 0

Reorder the terms:
(0.4 + x)(x + 3.2) = 0

Reorder the terms:
(0.4 + x)(3.2 + x) = 0

Multiply (0.4 + x) * (3.2 + x)
(0.4(3.2 + x) + x(3.2 + x)) = 0
((3.2 * 0.4 + x * 0.4) + x(3.2 + x)) = 0
((1.28 + 0.4x) + x(3.2 + x)) = 0
(1.28 + 0.4x + (3.2 * x + x * x)) = 0
(1.28 + 0.4x + (3.2x + x2)) = 0

Combine like terms: 0.4x + 3.2x = 3.6x
(1.28 + 3.6x + x2) = 0

Solving
1.28 + 3.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1.28' to each side of the equation.
1.28 + 3.6x + -1.28 + x2 = 0 + -1.28

Reorder the terms:
1.28 + -1.28 + 3.6x + x2 = 0 + -1.28

Combine like terms: 1.28 + -1.28 = 0.00
0.00 + 3.6x + x2 = 0 + -1.28
3.6x + x2 = 0 + -1.28

Combine like terms: 0 + -1.28 = -1.28
3.6x + x2 = -1.28

The x term is 3.6x.  Take half its coefficient (1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
3.6x + 3.24 + x2 = -1.28 + 3.24

Reorder the terms:
3.24 + 3.6x + x2 = -1.28 + 3.24

Combine like terms: -1.28 + 3.24 = 1.96
3.24 + 3.6x + x2 = 1.96

Factor a perfect square on the left side:
(x + 1.8)(x + 1.8) = 1.96

Calculate the square root of the right side: 1.4

Break this problem into two subproblems by setting 
(x + 1.8) equal to 1.4 and -1.4.


Subproblem 1
x + 1.8 = 1.4

Simplifying
x + 1.8 = 1.4

Reorder the terms:
1.8 + x = 1.4

Solving
1.8 + x = 1.4

Solving for variable 'x'.

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

Add '-1.8' to each side of the equation.
1.8 + -1.8 + x = 1.4 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + x = 1.4 + -1.8
x = 1.4 + -1.8

Combine like terms: 1.4 + -1.8 = -0.4
x = -0.4

Simplifying
x = -0.4


Subproblem 2
x + 1.8 = -1.4

Simplifying
x + 1.8 = -1.4

Reorder the terms:
1.8 + x = -1.4

Solving
1.8 + x = -1.4

Solving for variable 'x'.

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

Add '-1.8' to each side of the equation.
1.8 + -1.8 + x = -1.4 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + x = -1.4 + -1.8
x = -1.4 + -1.8

Combine like terms: -1.4 + -1.8 = -3.2
x = -3.2

Simplifying
x = -3.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.4, -3.2}

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