2a(25-a)(-8500)=1625000

Solution for 2a(25-a)(-8500)=1625000 equation:

Simplifying
2a(25 + -1a)(-8500) = 1625000

Reorder the terms for easier multiplication:
2 * -8500a(25 + -1a) = 1625000

Multiply 2 * -8500
-17000a(25 + -1a) = 1625000
(25 * -17000a + -1a * -17000a) = 1625000
(-425000a + 17000a2) = 1625000

Solving
-425000a + 17000a2 = 1625000

Solving for variable 'a'.

Reorder the terms:
-1625000 + -425000a + 17000a2 = 1625000 + -1625000

Combine like terms: 1625000 + -1625000 = 0
-1625000 + -425000a + 17000a2 = 0

Factor out the Greatest Common Factor (GCF), '1000'.
1000(-1625 + -425a + 17a2) = 0

Ignore the factor 1000.
Subproblem 1
Set the factor '(-1625 + -425a + 17a2)' equal to zero and attempt to solve:

Simplifying
-1625 + -425a + 17a2 = 0

Solving
-1625 + -425a + 17a2 = 0

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

Divide each side by '17'.
-95.58823529 + -25a + a2 = 0

Move the constant term to the right:

Add '95.58823529' to each side of the equation.
-95.58823529 + -25a + 95.58823529 + a2 = 0 + 95.58823529

Reorder the terms:
-95.58823529 + 95.58823529 + -25a + a2 = 0 + 95.58823529

Combine like terms: -95.58823529 + 95.58823529 = 0.00000000
0.00000000 + -25a + a2 = 0 + 95.58823529
-25a + a2 = 0 + 95.58823529

Combine like terms: 0 + 95.58823529 = 95.58823529
-25a + a2 = 95.58823529

The a term is -25a.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25a + 156.25 + a2 = 95.58823529 + 156.25

Reorder the terms:
156.25 + -25a + a2 = 95.58823529 + 156.25

Combine like terms: 95.58823529 + 156.25 = 251.83823529
156.25 + -25a + a2 = 251.83823529

Factor a perfect square on the left side:
(a + -12.5)(a + -12.5) = 251.83823529

Calculate the square root of the right side: 15.869411939

Break this problem into two subproblems by setting 
(a + -12.5) equal to 15.869411939 and -15.869411939.

Subproblem 1
a + -12.5 = 15.869411939

Simplifying
a + -12.5 = 15.869411939

Reorder the terms:
-12.5 + a = 15.869411939

Solving
-12.5 + a = 15.869411939

Solving for variable 'a'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + a = 15.869411939 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + a = 15.869411939 + 12.5
a = 15.869411939 + 12.5

Combine like terms: 15.869411939 + 12.5 = 28.369411939
a = 28.369411939

Simplifying
a = 28.369411939

Subproblem 2
a + -12.5 = -15.869411939

Simplifying
a + -12.5 = -15.869411939

Reorder the terms:
-12.5 + a = -15.869411939

Solving
-12.5 + a = -15.869411939

Solving for variable 'a'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + a = -15.869411939 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + a = -15.869411939 + 12.5
a = -15.869411939 + 12.5

Combine like terms: -15.869411939 + 12.5 = -3.369411939
a = -3.369411939

Simplifying
a = -3.369411939

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {28.369411939, -3.369411939}
Solution
a = {28.369411939, -3.369411939}