150s(225s-3.50)=2000

Solution for 150s(225s-3.50)=2000 equation:

Simplifying
150s(225s + -3.50) = 2000

Reorder the terms:
150s(-3.50 + 225s) = 2000
(-3.50 * 150s + 225s * 150s) = 2000
(-525s + 33750s2) = 2000

Solving
-525s + 33750s2 = 2000

Solving for variable 's'.

Reorder the terms:
-2000 + -525s + 33750s2 = 2000 + -2000

Combine like terms: 2000 + -2000 = 0
-2000 + -525s + 33750s2 = 0

Factor out the Greatest Common Factor (GCF), '25'.
25(-80 + -21s + 1350s2) = 0

Ignore the factor 25.
Subproblem 1
Set the factor '(-80 + -21s + 1350s2)' equal to zero and attempt to solve:

Simplifying
-80 + -21s + 1350s2 = 0

Solving
-80 + -21s + 1350s2 = 0

Begin completing the square.  Divide all terms by
1350 the coefficient of the squared term: 

Divide each side by '1350'.
-0.05925925926 + -0.01555555556s + s2 = 0.0

Move the constant term to the right:

Add '0.05925925926' to each side of the equation.
-0.05925925926 + -0.01555555556s + 0.05925925926 + s2 = 0.0 + 0.05925925926

Reorder the terms:
-0.05925925926 + 0.05925925926 + -0.01555555556s + s2 = 0.0 + 0.05925925926

Combine like terms: -0.05925925926 + 0.05925925926 = 0.00000000000
0.00000000000 + -0.01555555556s + s2 = 0.0 + 0.05925925926
-0.01555555556s + s2 = 0.0 + 0.05925925926

Combine like terms: 0.0 + 0.05925925926 = 0.05925925926
-0.01555555556s + s2 = 0.05925925926

The s term is -0.01555555556s.  Take half its coefficient (-0.00777777778).
Square it (0.00006049382720) and add it to both sides.

Add '0.00006049382720' to each side of the equation.
-0.01555555556s + 0.00006049382720 + s2 = 0.05925925926 + 0.00006049382720

Reorder the terms:
0.00006049382720 + -0.01555555556s + s2 = 0.05925925926 + 0.00006049382720

Combine like terms: 0.05925925926 + 0.00006049382720 = 0.0593197530872
0.00006049382720 + -0.01555555556s + s2 = 0.0593197530872

Factor a perfect square on the left side:
(s + -0.00777777778)(s + -0.00777777778) = 0.0593197530872

Calculate the square root of the right side: 0.243556468

Break this problem into two subproblems by setting 
(s + -0.00777777778) equal to 0.243556468 and -0.243556468.

Subproblem 1
s + -0.00777777778 = 0.243556468

Simplifying
s + -0.00777777778 = 0.243556468

Reorder the terms:
-0.00777777778 + s = 0.243556468

Solving
-0.00777777778 + s = 0.243556468

Solving for variable 's'.

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

Add '0.00777777778' to each side of the equation.
-0.00777777778 + 0.00777777778 + s = 0.243556468 + 0.00777777778

Combine like terms: -0.00777777778 + 0.00777777778 = 0.00000000000
0.00000000000 + s = 0.243556468 + 0.00777777778
s = 0.243556468 + 0.00777777778

Combine like terms: 0.243556468 + 0.00777777778 = 0.25133424578
s = 0.25133424578

Simplifying
s = 0.25133424578

Subproblem 2
s + -0.00777777778 = -0.243556468

Simplifying
s + -0.00777777778 = -0.243556468

Reorder the terms:
-0.00777777778 + s = -0.243556468

Solving
-0.00777777778 + s = -0.243556468

Solving for variable 's'.

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

Add '0.00777777778' to each side of the equation.
-0.00777777778 + 0.00777777778 + s = -0.243556468 + 0.00777777778

Combine like terms: -0.00777777778 + 0.00777777778 = 0.00000000000
0.00000000000 + s = -0.243556468 + 0.00777777778
s = -0.243556468 + 0.00777777778

Combine like terms: -0.243556468 + 0.00777777778 = -0.23577869022
s = -0.23577869022

Simplifying
s = -0.23577869022

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.25133424578, -0.23577869022}
Solution
s = {0.25133424578, -0.23577869022}