(6.4+x)*(5.6+x)=0

Solution for (6.4+x)*(5.6+x)=0 equation:

Simplifying
(6.4 + x)(5.6 + x) = 0

Multiply (6.4 + x) * (5.6 + x)
(6.4(5.6 + x) + x(5.6 + x)) = 0
((5.6 * 6.4 + x * 6.4) + x(5.6 + x)) = 0
((35.84 + 6.4x) + x(5.6 + x)) = 0
(35.84 + 6.4x + (5.6 * x + x * x)) = 0
(35.84 + 6.4x + (5.6x + x2)) = 0

Combine like terms: 6.4x + 5.6x = 12x
(35.84 + 12x + x2) = 0

Solving
35.84 + 12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-35.84' to each side of the equation.
35.84 + 12x + -35.84 + x2 = 0 + -35.84

Reorder the terms:
35.84 + -35.84 + 12x + x2 = 0 + -35.84

Combine like terms: 35.84 + -35.84 = 0.00
0.00 + 12x + x2 = 0 + -35.84
12x + x2 = 0 + -35.84

Combine like terms: 0 + -35.84 = -35.84
12x + x2 = -35.84

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = -35.84 + 36

Reorder the terms:
36 + 12x + x2 = -35.84 + 36

Combine like terms: -35.84 + 36 = 0.16
36 + 12x + x2 = 0.16

Factor a perfect square on the left side:
(x + 6)(x + 6) = 0.16

Calculate the square root of the right side: 0.4

Break this problem into two subproblems by setting 
(x + 6) equal to 0.4 and -0.4.

Subproblem 1
x + 6 = 0.4

Simplifying
x + 6 = 0.4

Reorder the terms:
6 + x = 0.4

Solving
6 + x = 0.4

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 0.4 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0.4 + -6
x = 0.4 + -6

Combine like terms: 0.4 + -6 = -5.6
x = -5.6

Simplifying
x = -5.6

Subproblem 2
x + 6 = -0.4

Simplifying
x + 6 = -0.4

Reorder the terms:
6 + x = -0.4

Solving
6 + x = -0.4

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -0.4 + -6

Combine like terms: 6 + -6 = 0
0 + x = -0.4 + -6
x = -0.4 + -6

Combine like terms: -0.4 + -6 = -6.4
x = -6.4

Simplifying
x = -6.4

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-5.6, -6.4}