(2x+5)(x)=240

Solution for (2x+5)(x)=240 equation:

Simplifying
(2x + 5)(x) = 240

Reorder the terms:
(5 + 2x)(x) = 240

Reorder the terms for easier multiplication:
x(5 + 2x) = 240
(5 * x + 2x * x) = 240
(5x + 2x2) = 240

Solving
5x + 2x2 = 240

Solving for variable 'x'.

Reorder the terms:
-240 + 5x + 2x2 = 240 + -240

Combine like terms: 240 + -240 = 0
-240 + 5x + 2x2 = 0

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

Divide each side by '2'.
-120 + 2.5x + x2 = 0

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + 2.5x + 120 + x2 = 0 + 120

Reorder the terms:
-120 + 120 + 2.5x + x2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + 2.5x + x2 = 0 + 120
2.5x + x2 = 0 + 120

Combine like terms: 0 + 120 = 120
2.5x + x2 = 120

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 = 120 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 120 + 1.5625

Combine like terms: 120 + 1.5625 = 121.5625
1.5625 + 2.5x + x2 = 121.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 121.5625

Calculate the square root of the right side: 11.025538536

Break this problem into two subproblems by setting 
(x + 1.25) equal to 11.025538536 and -11.025538536.

Subproblem 1
x + 1.25 = 11.025538536

Simplifying
x + 1.25 = 11.025538536

Reorder the terms:
1.25 + x = 11.025538536

Solving
1.25 + x = 11.025538536

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 = 11.025538536 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 11.025538536 + -1.25
x = 11.025538536 + -1.25

Combine like terms: 11.025538536 + -1.25 = 9.775538536
x = 9.775538536

Simplifying
x = 9.775538536

Subproblem 2
x + 1.25 = -11.025538536

Simplifying
x + 1.25 = -11.025538536

Reorder the terms:
1.25 + x = -11.025538536

Solving
1.25 + x = -11.025538536

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 = -11.025538536 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -11.025538536 + -1.25
x = -11.025538536 + -1.25

Combine like terms: -11.025538536 + -1.25 = -12.275538536
x = -12.275538536

Simplifying
x = -12.275538536

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.775538536, -12.275538536}