2(x+5)(x-2)-x(x+5)=140

Solution for 2(x+5)(x-2)-x(x+5)=140 equation:

Simplifying
2(x + 5)(x + -2) + -1x(x + 5) = 140

Reorder the terms:
2(5 + x)(x + -2) + -1x(x + 5) = 140

Reorder the terms:
2(5 + x)(-2 + x) + -1x(x + 5) = 140

Multiply (5 + x) * (-2 + x)
2(5(-2 + x) + x(-2 + x)) + -1x(x + 5) = 140
2((-2 * 5 + x * 5) + x(-2 + x)) + -1x(x + 5) = 140
2((-10 + 5x) + x(-2 + x)) + -1x(x + 5) = 140
2(-10 + 5x + (-2 * x + x * x)) + -1x(x + 5) = 140
2(-10 + 5x + (-2x + x2)) + -1x(x + 5) = 140

Combine like terms: 5x + -2x = 3x
2(-10 + 3x + x2) + -1x(x + 5) = 140
(-10 * 2 + 3x * 2 + x2 * 2) + -1x(x + 5) = 140
(-20 + 6x + 2x2) + -1x(x + 5) = 140

Reorder the terms:
-20 + 6x + 2x2 + -1x(5 + x) = 140
-20 + 6x + 2x2 + (5 * -1x + x * -1x) = 140
-20 + 6x + 2x2 + (-5x + -1x2) = 140

Reorder the terms:
-20 + 6x + -5x + 2x2 + -1x2 = 140

Combine like terms: 6x + -5x = 1x
-20 + 1x + 2x2 + -1x2 = 140

Combine like terms: 2x2 + -1x2 = 1x2
-20 + 1x + 1x2 = 140

Solving
-20 + 1x + 1x2 = 140

Solving for variable 'x'.

Reorder the terms:
-20 + -140 + 1x + 1x2 = 140 + -140

Combine like terms: -20 + -140 = -160
-160 + 1x + 1x2 = 140 + -140

Combine like terms: 140 + -140 = 0
-160 + 1x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '160' to each side of the equation.
-160 + 1x + 160 + x2 = 0 + 160

Reorder the terms:
-160 + 160 + 1x + x2 = 0 + 160

Combine like terms: -160 + 160 = 0
0 + 1x + x2 = 0 + 160
1x + x2 = 0 + 160

Combine like terms: 0 + 160 = 160
1x + x2 = 160

The x term is 1x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 160 + 0.25

Reorder the terms:
0.25 + x + x2 = 160 + 0.25

Combine like terms: 160 + 0.25 = 160.25
0.25 + x + x2 = 160.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 160.25

Calculate the square root of the right side: 12.658988901

Break this problem into two subproblems by setting 
(x + 0.5) equal to 12.658988901 and -12.658988901.

Subproblem 1
x + 0.5 = 12.658988901

Simplifying
x + 0.5 = 12.658988901

Reorder the terms:
0.5 + x = 12.658988901

Solving
0.5 + x = 12.658988901

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 12.658988901 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 12.658988901 + -0.5
x = 12.658988901 + -0.5

Combine like terms: 12.658988901 + -0.5 = 12.158988901
x = 12.158988901

Simplifying
x = 12.158988901

Subproblem 2
x + 0.5 = -12.658988901

Simplifying
x + 0.5 = -12.658988901

Reorder the terms:
0.5 + x = -12.658988901

Solving
0.5 + x = -12.658988901

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -12.658988901 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -12.658988901 + -0.5
x = -12.658988901 + -0.5

Combine like terms: -12.658988901 + -0.5 = -13.158988901
x = -13.158988901

Simplifying
x = -13.158988901

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.158988901, -13.158988901}