2(x+5)(x-2)=(x+52)

Solution for 2(x+5)(x-2)=(x+52) equation:

Simplifying
2(x + 5)(x + -2) = (x + 52)

Reorder the terms:
2(5 + x)(x + -2) = (x + 52)

Reorder the terms:
2(5 + x)(-2 + x) = (x + 52)

Multiply (5 + x) * (-2 + x)
2(5(-2 + x) + x(-2 + x)) = (x + 52)
2((-2 * 5 + x * 5) + x(-2 + x)) = (x + 52)
2((-10 + 5x) + x(-2 + x)) = (x + 52)
2(-10 + 5x + (-2 * x + x * x)) = (x + 52)
2(-10 + 5x + (-2x + x2)) = (x + 52)

Combine like terms: 5x + -2x = 3x
2(-10 + 3x + x2) = (x + 52)
(-10 * 2 + 3x * 2 + x2 * 2) = (x + 52)
(-20 + 6x + 2x2) = (x + 52)

Reorder the terms:
-20 + 6x + 2x2 = (52 + x)

Remove parenthesis around (52 + x)
-20 + 6x + 2x2 = 52 + x

Solving
-20 + 6x + 2x2 = 52 + x

Solving for variable 'x'.

Reorder the terms:
-20 + -52 + 6x + -1x + 2x2 = 52 + x + -52 + -1x

Combine like terms: -20 + -52 = -72
-72 + 6x + -1x + 2x2 = 52 + x + -52 + -1x

Combine like terms: 6x + -1x = 5x
-72 + 5x + 2x2 = 52 + x + -52 + -1x

Reorder the terms:
-72 + 5x + 2x2 = 52 + -52 + x + -1x

Combine like terms: 52 + -52 = 0
-72 + 5x + 2x2 = 0 + x + -1x
-72 + 5x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-72 + 5x + 2x2 = 0

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

Divide each side by '2'.
-36 + 2.5x + x2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 2.5x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 2.5x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 2.5x + x2 = 0 + 36
2.5x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
2.5x + x2 = 36

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 36 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 36 + 1.5625

Combine like terms: 36 + 1.5625 = 37.5625
1.5625 + 2.5x + x2 = 37.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 37.5625

Calculate the square root of the right side: 6.128825336

Break this problem into two subproblems by setting 
(x + 1.25) equal to 6.128825336 and -6.128825336.

Subproblem 1
x + 1.25 = 6.128825336

Simplifying
x + 1.25 = 6.128825336

Reorder the terms:
1.25 + x = 6.128825336

Solving
1.25 + x = 6.128825336

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 6.128825336 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 6.128825336 + -1.25
x = 6.128825336 + -1.25

Combine like terms: 6.128825336 + -1.25 = 4.878825336
x = 4.878825336

Simplifying
x = 4.878825336

Subproblem 2
x + 1.25 = -6.128825336

Simplifying
x + 1.25 = -6.128825336

Reorder the terms:
1.25 + x = -6.128825336

Solving
1.25 + x = -6.128825336

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -6.128825336 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -6.128825336 + -1.25
x = -6.128825336 + -1.25

Combine like terms: -6.128825336 + -1.25 = -7.378825336
x = -7.378825336

Simplifying
x = -7.378825336

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.878825336, -7.378825336}