3s^2-9s-3=21

Solution for 3s^2-9s-3=21 equation:

Simplifying
3s2 + -9s + -3 = 21

Reorder the terms:
-3 + -9s + 3s2 = 21

Solving
-3 + -9s + 3s2 = 21

Solving for variable 's'.

Reorder the terms:
-3 + -21 + -9s + 3s2 = 21 + -21

Combine like terms: -3 + -21 = -24
-24 + -9s + 3s2 = 21 + -21

Combine like terms: 21 + -21 = 0
-24 + -9s + 3s2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -3s + s2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-8 + -3s + s2)' equal to zero and attempt to solve:

Simplifying
-8 + -3s + s2 = 0

Solving
-8 + -3s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -3s + 8 + s2 = 0 + 8

Reorder the terms:
-8 + 8 + -3s + s2 = 0 + 8

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

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

The s term is -3s.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3s + 2.25 + s2 = 8 + 2.25

Reorder the terms:
2.25 + -3s + s2 = 8 + 2.25

Combine like terms: 8 + 2.25 = 10.25
2.25 + -3s + s2 = 10.25

Factor a perfect square on the left side:
(s + -1.5)(s + -1.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(s + -1.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
s + -1.5 = 3.201562119

Simplifying
s + -1.5 = 3.201562119

Reorder the terms:
-1.5 + s = 3.201562119

Solving
-1.5 + s = 3.201562119

Solving for variable 's'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + s = 3.201562119 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + s = 3.201562119 + 1.5
s = 3.201562119 + 1.5

Combine like terms: 3.201562119 + 1.5 = 4.701562119
s = 4.701562119

Simplifying
s = 4.701562119

Subproblem 2
s + -1.5 = -3.201562119

Simplifying
s + -1.5 = -3.201562119

Reorder the terms:
-1.5 + s = -3.201562119

Solving
-1.5 + s = -3.201562119

Solving for variable 's'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + s = -3.201562119 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + s = -3.201562119 + 1.5
s = -3.201562119 + 1.5

Combine like terms: -3.201562119 + 1.5 = -1.701562119
s = -1.701562119

Simplifying
s = -1.701562119

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {4.701562119, -1.701562119}
Solution
s = {4.701562119, -1.701562119}