6=(7-2x)(3-2x)

Solution for 6=(7-2x)(3-2x) equation:

Simplifying
6 = (7 + -2x)(3 + -2x)

Multiply (7 + -2x) * (3 + -2x)
6 = (7(3 + -2x) + -2x * (3 + -2x))
6 = ((3 * 7 + -2x * 7) + -2x * (3 + -2x))
6 = ((21 + -14x) + -2x * (3 + -2x))
6 = (21 + -14x + (3 * -2x + -2x * -2x))
6 = (21 + -14x + (-6x + 4x2))

Combine like terms: -14x + -6x = -20x
6 = (21 + -20x + 4x2)

Solving
6 = 21 + -20x + 4x2

Solving for variable 'x'.

Combine like terms: 6 + -21 = -15
-15 + 20x + -4x2 = 21 + -20x + 4x2 + -21 + 20x + -4x2

Reorder the terms:
-15 + 20x + -4x2 = 21 + -21 + -20x + 20x + 4x2 + -4x2

Combine like terms: 21 + -21 = 0
-15 + 20x + -4x2 = 0 + -20x + 20x + 4x2 + -4x2
-15 + 20x + -4x2 = -20x + 20x + 4x2 + -4x2

Combine like terms: -20x + 20x = 0
-15 + 20x + -4x2 = 0 + 4x2 + -4x2
-15 + 20x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-15 + 20x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
3.75 + -5x + x2 = 0

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + -5x + -3.75 + x2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + -5x + x2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + -5x + x2 = 0 + -3.75
-5x + x2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
-5x + x2 = -3.75

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -3.75 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -3.75 + 6.25

Combine like terms: -3.75 + 6.25 = 2.5
6.25 + -5x + x2 = 2.5

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 2.5

Calculate the square root of the right side: 1.58113883

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.58113883 and -1.58113883.

Subproblem 1
x + -2.5 = 1.58113883

Simplifying
x + -2.5 = 1.58113883

Reorder the terms:
-2.5 + x = 1.58113883

Solving
-2.5 + x = 1.58113883

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 1.58113883 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 1.58113883 + 2.5
x = 1.58113883 + 2.5

Combine like terms: 1.58113883 + 2.5 = 4.08113883
x = 4.08113883

Simplifying
x = 4.08113883

Subproblem 2
x + -2.5 = -1.58113883

Simplifying
x + -2.5 = -1.58113883

Reorder the terms:
-2.5 + x = -1.58113883

Solving
-2.5 + x = -1.58113883

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -1.58113883 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -1.58113883 + 2.5
x = -1.58113883 + 2.5

Combine like terms: -1.58113883 + 2.5 = 0.91886117
x = 0.91886117

Simplifying
x = 0.91886117

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.08113883, 0.91886117}