(3.2-x)(5.2-x)=0

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Solution for (3.2-x)(5.2-x)=0 equation: 


Simplifying
(3.2 + -1x)(5.2 + -1x) = 0

Multiply (3.2 + -1x) * (5.2 + -1x)
(3.2(5.2 + -1x) + -1x * (5.2 + -1x)) = 0
((5.2 * 3.2 + -1x * 3.2) + -1x * (5.2 + -1x)) = 0
((16.64 + -3.2x) + -1x * (5.2 + -1x)) = 0
(16.64 + -3.2x + (5.2 * -1x + -1x * -1x)) = 0
(16.64 + -3.2x + (-5.2x + 1x2)) = 0

Combine like terms: -3.2x + -5.2x = -8.4x
(16.64 + -8.4x + 1x2) = 0

Solving
16.64 + -8.4x + 1x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-16.64' to each side of the equation.
16.64 + -8.4x + -16.64 + x2 = 0 + -16.64

Reorder the terms:
16.64 + -16.64 + -8.4x + x2 = 0 + -16.64

Combine like terms: 16.64 + -16.64 = 0.00
0.00 + -8.4x + x2 = 0 + -16.64
-8.4x + x2 = 0 + -16.64

Combine like terms: 0 + -16.64 = -16.64
-8.4x + x2 = -16.64

The x term is -8.4x.  Take half its coefficient (-4.2).
Square it (17.64) and add it to both sides.

Add '17.64' to each side of the equation.
-8.4x + 17.64 + x2 = -16.64 + 17.64

Reorder the terms:
17.64 + -8.4x + x2 = -16.64 + 17.64

Combine like terms: -16.64 + 17.64 = 1
17.64 + -8.4x + x2 = 1

Factor a perfect square on the left side:
(x + -4.2)(x + -4.2) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + -4.2) equal to 1 and -1.


Subproblem 1
x + -4.2 = 1

Simplifying
x + -4.2 = 1

Reorder the terms:
-4.2 + x = 1

Solving
-4.2 + x = 1

Solving for variable 'x'.

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

Add '4.2' to each side of the equation.
-4.2 + 4.2 + x = 1 + 4.2

Combine like terms: -4.2 + 4.2 = 0.0
0.0 + x = 1 + 4.2
x = 1 + 4.2

Combine like terms: 1 + 4.2 = 5.2
x = 5.2

Simplifying
x = 5.2


Subproblem 2
x + -4.2 = -1

Simplifying
x + -4.2 = -1

Reorder the terms:
-4.2 + x = -1

Solving
-4.2 + x = -1

Solving for variable 'x'.

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

Add '4.2' to each side of the equation.
-4.2 + 4.2 + x = -1 + 4.2

Combine like terms: -4.2 + 4.2 = 0.0
0.0 + x = -1 + 4.2
x = -1 + 4.2

Combine like terms: -1 + 4.2 = 3.2
x = 3.2

Simplifying
x = 3.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.2, 3.2}

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