3s(s-2)=15

Solution for 3s(s-2)=15 equation:

Simplifying
3s(s + -2) = 15

Reorder the terms:
3s(-2 + s) = 15
(-2 * 3s + s * 3s) = 15
(-6s + 3s2) = 15

Solving
-6s + 3s2 = 15

Solving for variable 's'.

Reorder the terms:
-15 + -6s + 3s2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + -6s + 3s2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -2s + s2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -2s + s2)' equal to zero and attempt to solve:

Simplifying
-5 + -2s + s2 = 0

Solving
-5 + -2s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -2s + 5 + s2 = 0 + 5

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

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

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

The s term is -2s.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2s + 1 + s2 = 5 + 1

Reorder the terms:
1 + -2s + s2 = 5 + 1

Combine like terms: 5 + 1 = 6
1 + -2s + s2 = 6

Factor a perfect square on the left side:
(s + -1)(s + -1) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(s + -1) equal to 2.449489743 and -2.449489743.

Subproblem 1
s + -1 = 2.449489743

Simplifying
s + -1 = 2.449489743

Reorder the terms:
-1 + s = 2.449489743

Solving
-1 + s = 2.449489743

Solving for variable 's'.

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

Add '1' to each side of the equation.
-1 + 1 + s = 2.449489743 + 1

Combine like terms: -1 + 1 = 0
0 + s = 2.449489743 + 1
s = 2.449489743 + 1

Combine like terms: 2.449489743 + 1 = 3.449489743
s = 3.449489743

Simplifying
s = 3.449489743

Subproblem 2
s + -1 = -2.449489743

Simplifying
s + -1 = -2.449489743

Reorder the terms:
-1 + s = -2.449489743

Solving
-1 + s = -2.449489743

Solving for variable 's'.

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

Add '1' to each side of the equation.
-1 + 1 + s = -2.449489743 + 1

Combine like terms: -1 + 1 = 0
0 + s = -2.449489743 + 1
s = -2.449489743 + 1

Combine like terms: -2.449489743 + 1 = -1.449489743
s = -1.449489743

Simplifying
s = -1.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {3.449489743, -1.449489743}
Solution
s = {3.449489743, -1.449489743}