(5s^2-3s)-(2s^2-7s)+(5s^2-6)=0

Solution for (5s^2-3s)-(2s^2-7s)+(5s^2-6)=0 equation:

Simplifying
(5s2 + -3s) + -1(2s2 + -7s) + (5s2 + -6) = 0

Reorder the terms:
(-3s + 5s2) + -1(2s2 + -7s) + (5s2 + -6) = 0

Remove parenthesis around (-3s + 5s2)
-3s + 5s2 + -1(2s2 + -7s) + (5s2 + -6) = 0

Reorder the terms:
-3s + 5s2 + -1(-7s + 2s2) + (5s2 + -6) = 0
-3s + 5s2 + (-7s * -1 + 2s2 * -1) + (5s2 + -6) = 0
-3s + 5s2 + (7s + -2s2) + (5s2 + -6) = 0

Reorder the terms:
-3s + 5s2 + 7s + -2s2 + (-6 + 5s2) = 0

Remove parenthesis around (-6 + 5s2)
-3s + 5s2 + 7s + -2s2 + -6 + 5s2 = 0

Reorder the terms:
-6 + -3s + 7s + 5s2 + -2s2 + 5s2 = 0

Combine like terms: -3s + 7s = 4s
-6 + 4s + 5s2 + -2s2 + 5s2 = 0

Combine like terms: 5s2 + -2s2 = 3s2
-6 + 4s + 3s2 + 5s2 = 0

Combine like terms: 3s2 + 5s2 = 8s2
-6 + 4s + 8s2 = 0

Solving
-6 + 4s + 8s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 2s + 4s2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 2s + 4s2)' equal to zero and attempt to solve:

Simplifying
-3 + 2s + 4s2 = 0

Solving
-3 + 2s + 4s2 = 0

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

Divide each side by '4'.
-0.75 + 0.5s + s2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 0.5s + 0.75 + s2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 0.5s + s2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 0.5s + s2 = 0 + 0.75
0.5s + s2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
0.5s + s2 = 0.75

The s term is 0.5s.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5s + 0.0625 + s2 = 0.75 + 0.0625

Reorder the terms:
0.0625 + 0.5s + s2 = 0.75 + 0.0625

Combine like terms: 0.75 + 0.0625 = 0.8125
0.0625 + 0.5s + s2 = 0.8125

Factor a perfect square on the left side:
(s + 0.25)(s + 0.25) = 0.8125

Calculate the square root of the right side: 0.901387819

Break this problem into two subproblems by setting 
(s + 0.25) equal to 0.901387819 and -0.901387819.

Subproblem 1
s + 0.25 = 0.901387819

Simplifying
s + 0.25 = 0.901387819

Reorder the terms:
0.25 + s = 0.901387819

Solving
0.25 + s = 0.901387819

Solving for variable 's'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + s = 0.901387819 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + s = 0.901387819 + -0.25
s = 0.901387819 + -0.25

Combine like terms: 0.901387819 + -0.25 = 0.651387819
s = 0.651387819

Simplifying
s = 0.651387819

Subproblem 2
s + 0.25 = -0.901387819

Simplifying
s + 0.25 = -0.901387819

Reorder the terms:
0.25 + s = -0.901387819

Solving
0.25 + s = -0.901387819

Solving for variable 's'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + s = -0.901387819 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + s = -0.901387819 + -0.25
s = -0.901387819 + -0.25

Combine like terms: -0.901387819 + -0.25 = -1.151387819
s = -1.151387819

Simplifying
s = -1.151387819

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {0.651387819, -1.151387819}
Solution
s = {0.651387819, -1.151387819}