2(2x+5)*2x=250

Solution for 2(2x+5)*2x=250 equation:

Simplifying
2(2x + 5) * 2x = 250

Reorder the terms:
2(5 + 2x) * 2x = 250

Reorder the terms for easier multiplication:
2 * 2x(5 + 2x) = 250

Multiply 2 * 2
4x(5 + 2x) = 250
(5 * 4x + 2x * 4x) = 250
(20x + 8x2) = 250

Solving
20x + 8x2 = 250

Solving for variable 'x'.

Reorder the terms:
-250 + 20x + 8x2 = 250 + -250

Combine like terms: 250 + -250 = 0
-250 + 20x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-125 + 10x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-125 + 10x + 4x2)' equal to zero and attempt to solve:

Simplifying
-125 + 10x + 4x2 = 0

Solving
-125 + 10x + 4x2 = 0

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

Divide each side by '4'.
-31.25 + 2.5x + x2 = 0

Move the constant term to the right:

Add '31.25' to each side of the equation.
-31.25 + 2.5x + 31.25 + x2 = 0 + 31.25

Reorder the terms:
-31.25 + 31.25 + 2.5x + x2 = 0 + 31.25

Combine like terms: -31.25 + 31.25 = 0.00
0.00 + 2.5x + x2 = 0 + 31.25
2.5x + x2 = 0 + 31.25

Combine like terms: 0 + 31.25 = 31.25
2.5x + x2 = 31.25

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 = 31.25 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 31.25 + 1.5625

Combine like terms: 31.25 + 1.5625 = 32.8125
1.5625 + 2.5x + x2 = 32.8125

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 32.8125

Calculate the square root of the right side: 5.728219619

Break this problem into two subproblems by setting 
(x + 1.25) equal to 5.728219619 and -5.728219619.

Subproblem 1
x + 1.25 = 5.728219619

Simplifying
x + 1.25 = 5.728219619

Reorder the terms:
1.25 + x = 5.728219619

Solving
1.25 + x = 5.728219619

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 = 5.728219619 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 5.728219619 + -1.25
x = 5.728219619 + -1.25

Combine like terms: 5.728219619 + -1.25 = 4.478219619
x = 4.478219619

Simplifying
x = 4.478219619

Subproblem 2
x + 1.25 = -5.728219619

Simplifying
x + 1.25 = -5.728219619

Reorder the terms:
1.25 + x = -5.728219619

Solving
1.25 + x = -5.728219619

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 = -5.728219619 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -5.728219619 + -1.25
x = -5.728219619 + -1.25

Combine like terms: -5.728219619 + -1.25 = -6.978219619
x = -6.978219619

Simplifying
x = -6.978219619

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.478219619, -6.978219619}
Solution
x = {4.478219619, -6.978219619}