4(x-2)92(-x+3)=1

Solution for 4(x-2)92(-x+3)=1 equation:

Simplifying
4(x + -2) * 92(-1x + 3) = 1

Reorder the terms:
4(-2 + x) * 92(-1x + 3) = 1

Reorder the terms:
4(-2 + x) * 92(3 + -1x) = 1

Reorder the terms for easier multiplication:
4 * 92(-2 + x)(3 + -1x) = 1

Multiply 4 * 92
368(-2 + x)(3 + -1x) = 1

Multiply (-2 + x) * (3 + -1x)
368(-2(3 + -1x) + x(3 + -1x)) = 1
368((3 * -2 + -1x * -2) + x(3 + -1x)) = 1
368((-6 + 2x) + x(3 + -1x)) = 1
368(-6 + 2x + (3 * x + -1x * x)) = 1
368(-6 + 2x + (3x + -1x2)) = 1

Combine like terms: 2x + 3x = 5x
368(-6 + 5x + -1x2) = 1
(-6 * 368 + 5x * 368 + -1x2 * 368) = 1
(-2208 + 1840x + -368x2) = 1

Solving
-2208 + 1840x + -368x2 = 1

Solving for variable 'x'.

Reorder the terms:
-2208 + -1 + 1840x + -368x2 = 1 + -1

Combine like terms: -2208 + -1 = -2209
-2209 + 1840x + -368x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-2209 + 1840x + -368x2 = 0

Begin completing the square.  Divide all terms by
-368 the coefficient of the squared term: 

Divide each side by '-368'.
6.002717391 + -5x + x2 = 0

Move the constant term to the right:

Add '-6.002717391' to each side of the equation.
6.002717391 + -5x + -6.002717391 + x2 = 0 + -6.002717391

Reorder the terms:
6.002717391 + -6.002717391 + -5x + x2 = 0 + -6.002717391

Combine like terms: 6.002717391 + -6.002717391 = 0.000000000
0.000000000 + -5x + x2 = 0 + -6.002717391
-5x + x2 = 0 + -6.002717391

Combine like terms: 0 + -6.002717391 = -6.002717391
-5x + x2 = -6.002717391

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 = -6.002717391 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -6.002717391 + 6.25

Combine like terms: -6.002717391 + 6.25 = 0.247282609
6.25 + -5x + x2 = 0.247282609

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 0.247282609

Calculate the square root of the right side: 0.497275184

Break this problem into two subproblems by setting 
(x + -2.5) equal to 0.497275184 and -0.497275184.

Subproblem 1
x + -2.5 = 0.497275184

Simplifying
x + -2.5 = 0.497275184

Reorder the terms:
-2.5 + x = 0.497275184

Solving
-2.5 + x = 0.497275184

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 = 0.497275184 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 0.497275184 + 2.5
x = 0.497275184 + 2.5

Combine like terms: 0.497275184 + 2.5 = 2.997275184
x = 2.997275184

Simplifying
x = 2.997275184

Subproblem 2
x + -2.5 = -0.497275184

Simplifying
x + -2.5 = -0.497275184

Reorder the terms:
-2.5 + x = -0.497275184

Solving
-2.5 + x = -0.497275184

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 = -0.497275184 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -0.497275184 + 2.5
x = -0.497275184 + 2.5

Combine like terms: -0.497275184 + 2.5 = 2.002724816
x = 2.002724816

Simplifying
x = 2.002724816

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.997275184, 2.002724816}