(x-0.4)*(x-0.6)=5

Solution for (x-0.4)*(x-0.6)=5 equation:

Simplifying
(x + -0.4)(x + -0.6) = 5

Reorder the terms:
(-0.4 + x)(x + -0.6) = 5

Reorder the terms:
(-0.4 + x)(-0.6 + x) = 5

Multiply (-0.4 + x) * (-0.6 + x)
(-0.4(-0.6 + x) + x(-0.6 + x)) = 5
((-0.6 * -0.4 + x * -0.4) + x(-0.6 + x)) = 5
((0.24 + -0.4x) + x(-0.6 + x)) = 5
(0.24 + -0.4x + (-0.6 * x + x * x)) = 5
(0.24 + -0.4x + (-0.6x + x2)) = 5

Combine like terms: -0.4x + -0.6x = -1x
(0.24 + -1x + x2) = 5

Solving
0.24 + -1x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
0.24 + -5 + -1x + x2 = 5 + -5

Combine like terms: 0.24 + -5 = -4.76
-4.76 + -1x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-4.76 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4.76' to each side of the equation.
-4.76 + -1x + 4.76 + x2 = 0 + 4.76

Reorder the terms:
-4.76 + 4.76 + -1x + x2 = 0 + 4.76

Combine like terms: -4.76 + 4.76 = 0.00
0.00 + -1x + x2 = 0 + 4.76
-1x + x2 = 0 + 4.76

Combine like terms: 0 + 4.76 = 4.76
-1x + x2 = 4.76

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 4.76 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 4.76 + 0.25

Combine like terms: 4.76 + 0.25 = 5.01
0.25 + -1x + x2 = 5.01

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 5.01

Calculate the square root of the right side: 2.238302929

Break this problem into two subproblems by setting 
(x + -0.5) equal to 2.238302929 and -2.238302929.

Subproblem 1
x + -0.5 = 2.238302929

Simplifying
x + -0.5 = 2.238302929

Reorder the terms:
-0.5 + x = 2.238302929

Solving
-0.5 + x = 2.238302929

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 2.238302929 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 2.238302929 + 0.5
x = 2.238302929 + 0.5

Combine like terms: 2.238302929 + 0.5 = 2.738302929
x = 2.738302929

Simplifying
x = 2.738302929

Subproblem 2
x + -0.5 = -2.238302929

Simplifying
x + -0.5 = -2.238302929

Reorder the terms:
-0.5 + x = -2.238302929

Solving
-0.5 + x = -2.238302929

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -2.238302929 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -2.238302929 + 0.5
x = -2.238302929 + 0.5

Combine like terms: -2.238302929 + 0.5 = -1.738302929
x = -1.738302929

Simplifying
x = -1.738302929

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.738302929, -1.738302929}