(9-2x)*(6-2x)=50

Solution for (9-2x)*(6-2x)=50 equation:

Simplifying
(9 + -2x)(6 + -2x) = 50

Multiply (9 + -2x) * (6 + -2x)
(9(6 + -2x) + -2x * (6 + -2x)) = 50
((6 * 9 + -2x * 9) + -2x * (6 + -2x)) = 50
((54 + -18x) + -2x * (6 + -2x)) = 50
(54 + -18x + (6 * -2x + -2x * -2x)) = 50
(54 + -18x + (-12x + 4x2)) = 50

Combine like terms: -18x + -12x = -30x
(54 + -30x + 4x2) = 50

Solving
54 + -30x + 4x2 = 50

Solving for variable 'x'.

Reorder the terms:
54 + -50 + -30x + 4x2 = 50 + -50

Combine like terms: 54 + -50 = 4
4 + -30x + 4x2 = 50 + -50

Combine like terms: 50 + -50 = 0
4 + -30x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -15x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -15x + 2x2)' equal to zero and attempt to solve:

Simplifying
2 + -15x + 2x2 = 0

Solving
2 + -15x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
1 + -7.5x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -7.5x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -7.5x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7.5x + x2 = 0 + -1
-7.5x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-7.5x + x2 = -1

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = -1 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = -1 + 14.0625

Combine like terms: -1 + 14.0625 = 13.0625
14.0625 + -7.5x + x2 = 13.0625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 13.0625

Calculate the square root of the right side: 3.614208074

Break this problem into two subproblems by setting 
(x + -3.75) equal to 3.614208074 and -3.614208074.

Subproblem 1
x + -3.75 = 3.614208074

Simplifying
x + -3.75 = 3.614208074

Reorder the terms:
-3.75 + x = 3.614208074

Solving
-3.75 + x = 3.614208074

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 3.614208074 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 3.614208074 + 3.75
x = 3.614208074 + 3.75

Combine like terms: 3.614208074 + 3.75 = 7.364208074
x = 7.364208074

Simplifying
x = 7.364208074

Subproblem 2
x + -3.75 = -3.614208074

Simplifying
x + -3.75 = -3.614208074

Reorder the terms:
-3.75 + x = -3.614208074

Solving
-3.75 + x = -3.614208074

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -3.614208074 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -3.614208074 + 3.75
x = -3.614208074 + 3.75

Combine like terms: -3.614208074 + 3.75 = 0.135791926
x = 0.135791926

Simplifying
x = 0.135791926

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.364208074, 0.135791926}
Solution
x = {7.364208074, 0.135791926}