25x+50x(2x-40)=13000

Solution for 25x+50x(2x-40)=13000 equation:

Simplifying
25x + 50x(2x + -40) = 13000

Reorder the terms:
25x + 50x(-40 + 2x) = 13000
25x + (-40 * 50x + 2x * 50x) = 13000
25x + (-2000x + 100x2) = 13000

Combine like terms: 25x + -2000x = -1975x
-1975x + 100x2 = 13000

Solving
-1975x + 100x2 = 13000

Solving for variable 'x'.

Reorder the terms:
-13000 + -1975x + 100x2 = 13000 + -13000

Combine like terms: 13000 + -13000 = 0
-13000 + -1975x + 100x2 = 0

Factor out the Greatest Common Factor (GCF), '25'.
25(-520 + -79x + 4x2) = 0

Ignore the factor 25.
Subproblem 1
Set the factor '(-520 + -79x + 4x2)' equal to zero and attempt to solve:

Simplifying
-520 + -79x + 4x2 = 0

Solving
-520 + -79x + 4x2 = 0

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

Divide each side by '4'.
-130 + -19.75x + x2 = 0

Move the constant term to the right:

Add '130' to each side of the equation.
-130 + -19.75x + 130 + x2 = 0 + 130

Reorder the terms:
-130 + 130 + -19.75x + x2 = 0 + 130

Combine like terms: -130 + 130 = 0
0 + -19.75x + x2 = 0 + 130
-19.75x + x2 = 0 + 130

Combine like terms: 0 + 130 = 130
-19.75x + x2 = 130

The x term is -19.75x.  Take half its coefficient (-9.875).
Square it (97.515625) and add it to both sides.

Add '97.515625' to each side of the equation.
-19.75x + 97.515625 + x2 = 130 + 97.515625

Reorder the terms:
97.515625 + -19.75x + x2 = 130 + 97.515625

Combine like terms: 130 + 97.515625 = 227.515625
97.515625 + -19.75x + x2 = 227.515625

Factor a perfect square on the left side:
(x + -9.875)(x + -9.875) = 227.515625

Calculate the square root of the right side: 15.083621084

Break this problem into two subproblems by setting 
(x + -9.875) equal to 15.083621084 and -15.083621084.

Subproblem 1
x + -9.875 = 15.083621084

Simplifying
x + -9.875 = 15.083621084

Reorder the terms:
-9.875 + x = 15.083621084

Solving
-9.875 + x = 15.083621084

Solving for variable 'x'.

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

Add '9.875' to each side of the equation.
-9.875 + 9.875 + x = 15.083621084 + 9.875

Combine like terms: -9.875 + 9.875 = 0.000
0.000 + x = 15.083621084 + 9.875
x = 15.083621084 + 9.875

Combine like terms: 15.083621084 + 9.875 = 24.958621084
x = 24.958621084

Simplifying
x = 24.958621084

Subproblem 2
x + -9.875 = -15.083621084

Simplifying
x + -9.875 = -15.083621084

Reorder the terms:
-9.875 + x = -15.083621084

Solving
-9.875 + x = -15.083621084

Solving for variable 'x'.

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

Add '9.875' to each side of the equation.
-9.875 + 9.875 + x = -15.083621084 + 9.875

Combine like terms: -9.875 + 9.875 = 0.000
0.000 + x = -15.083621084 + 9.875
x = -15.083621084 + 9.875

Combine like terms: -15.083621084 + 9.875 = -5.208621084
x = -5.208621084

Simplifying
x = -5.208621084

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.958621084, -5.208621084}
Solution
x = {24.958621084, -5.208621084}