(10-2x)(8-2x)=60

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Solution for (10-2x)(8-2x)=60 equation: 


Simplifying
(10 + -2x)(8 + -2x) = 60

Multiply (10 + -2x) * (8 + -2x)
(10(8 + -2x) + -2x * (8 + -2x)) = 60
((8 * 10 + -2x * 10) + -2x * (8 + -2x)) = 60
((80 + -20x) + -2x * (8 + -2x)) = 60
(80 + -20x + (8 * -2x + -2x * -2x)) = 60
(80 + -20x + (-16x + 4x2)) = 60

Combine like terms: -20x + -16x = -36x
(80 + -36x + 4x2) = 60

Solving
80 + -36x + 4x2 = 60

Solving for variable 'x'.

Reorder the terms:
80 + -60 + -36x + 4x2 = 60 + -60

Combine like terms: 80 + -60 = 20
20 + -36x + 4x2 = 60 + -60

Combine like terms: 60 + -60 = 0
20 + -36x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + -9x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(5 + -9x + x2)' equal to zero and attempt to solve:

Simplifying
5 + -9x + x2 = 0

Solving
5 + -9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -9x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -9x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -9x + x2 = 0 + -5
-9x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-9x + x2 = -5

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -5 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -5 + 20.25

Combine like terms: -5 + 20.25 = 15.25
20.25 + -9x + x2 = 15.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + -4.5) equal to 3.905124838 and -3.905124838.


Subproblem 1
x + -4.5 = 3.905124838

Simplifying
x + -4.5 = 3.905124838

Reorder the terms:
-4.5 + x = 3.905124838

Solving
-4.5 + x = 3.905124838

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 3.905124838 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 3.905124838 + 4.5
x = 3.905124838 + 4.5

Combine like terms: 3.905124838 + 4.5 = 8.405124838
x = 8.405124838

Simplifying
x = 8.405124838


Subproblem 2
x + -4.5 = -3.905124838

Simplifying
x + -4.5 = -3.905124838

Reorder the terms:
-4.5 + x = -3.905124838

Solving
-4.5 + x = -3.905124838

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -3.905124838 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -3.905124838 + 4.5
x = -3.905124838 + 4.5

Combine like terms: -3.905124838 + 4.5 = 0.594875162
x = 0.594875162

Simplifying
x = 0.594875162


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.405124838, 0.594875162}
Solution
x = {8.405124838, 0.594875162}

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