(40-x)2(x-5)+7=x

Solution for (40-x)2(x-5)+7=x equation:

Simplifying
(40 + -1x) * 2(x + -5) + 7 = x

Reorder the terms:
(40 + -1x) * 2(-5 + x) + 7 = x

Reorder the terms for easier multiplication:
2(40 + -1x)(-5 + x) + 7 = x

Multiply (40 + -1x) * (-5 + x)
2(40(-5 + x) + -1x * (-5 + x)) + 7 = x
2((-5 * 40 + x * 40) + -1x * (-5 + x)) + 7 = x
2((-200 + 40x) + -1x * (-5 + x)) + 7 = x
2(-200 + 40x + (-5 * -1x + x * -1x)) + 7 = x
2(-200 + 40x + (5x + -1x2)) + 7 = x

Combine like terms: 40x + 5x = 45x
2(-200 + 45x + -1x2) + 7 = x
(-200 * 2 + 45x * 2 + -1x2 * 2) + 7 = x
(-400 + 90x + -2x2) + 7 = x

Reorder the terms:
-400 + 7 + 90x + -2x2 = x

Combine like terms: -400 + 7 = -393
-393 + 90x + -2x2 = x

Solving
-393 + 90x + -2x2 = x

Solving for variable 'x'.

Reorder the terms:
-393 + 90x + -1x + -2x2 = x + -1x

Combine like terms: 90x + -1x = 89x
-393 + 89x + -2x2 = x + -1x

Combine like terms: x + -1x = 0
-393 + 89x + -2x2 = 0

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

Divide each side by '-2'.
196.5 + -44.5x + x2 = 0

Move the constant term to the right:

Add '-196.5' to each side of the equation.
196.5 + -44.5x + -196.5 + x2 = 0 + -196.5

Reorder the terms:
196.5 + -196.5 + -44.5x + x2 = 0 + -196.5

Combine like terms: 196.5 + -196.5 = 0.0
0.0 + -44.5x + x2 = 0 + -196.5
-44.5x + x2 = 0 + -196.5

Combine like terms: 0 + -196.5 = -196.5
-44.5x + x2 = -196.5

The x term is -44.5x.  Take half its coefficient (-22.25).
Square it (495.0625) and add it to both sides.

Add '495.0625' to each side of the equation.
-44.5x + 495.0625 + x2 = -196.5 + 495.0625

Reorder the terms:
495.0625 + -44.5x + x2 = -196.5 + 495.0625

Combine like terms: -196.5 + 495.0625 = 298.5625
495.0625 + -44.5x + x2 = 298.5625

Factor a perfect square on the left side:
(x + -22.25)(x + -22.25) = 298.5625

Calculate the square root of the right side: 17.278961196

Break this problem into two subproblems by setting 
(x + -22.25) equal to 17.278961196 and -17.278961196.

Subproblem 1
x + -22.25 = 17.278961196

Simplifying
x + -22.25 = 17.278961196

Reorder the terms:
-22.25 + x = 17.278961196

Solving
-22.25 + x = 17.278961196

Solving for variable 'x'.

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

Add '22.25' to each side of the equation.
-22.25 + 22.25 + x = 17.278961196 + 22.25

Combine like terms: -22.25 + 22.25 = 0.00
0.00 + x = 17.278961196 + 22.25
x = 17.278961196 + 22.25

Combine like terms: 17.278961196 + 22.25 = 39.528961196
x = 39.528961196

Simplifying
x = 39.528961196

Subproblem 2
x + -22.25 = -17.278961196

Simplifying
x + -22.25 = -17.278961196

Reorder the terms:
-22.25 + x = -17.278961196

Solving
-22.25 + x = -17.278961196

Solving for variable 'x'.

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

Add '22.25' to each side of the equation.
-22.25 + 22.25 + x = -17.278961196 + 22.25

Combine like terms: -22.25 + 22.25 = 0.00
0.00 + x = -17.278961196 + 22.25
x = -17.278961196 + 22.25

Combine like terms: -17.278961196 + 22.25 = 4.971038804
x = 4.971038804

Simplifying
x = 4.971038804

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {39.528961196, 4.971038804}