2s(s-5)=2(s+5)

Solution for 2s(s-5)=2(s+5) equation:

Simplifying
2s(s + -5) = 2(s + 5)

Reorder the terms:
2s(-5 + s) = 2(s + 5)
(-5 * 2s + s * 2s) = 2(s + 5)
(-10s + 2s2) = 2(s + 5)

Reorder the terms:
-10s + 2s2 = 2(5 + s)
-10s + 2s2 = (5 * 2 + s * 2)
-10s + 2s2 = (10 + 2s)

Solving
-10s + 2s2 = 10 + 2s

Solving for variable 's'.

Reorder the terms:
-10 + -10s + -2s + 2s2 = 10 + 2s + -10 + -2s

Combine like terms: -10s + -2s = -12s
-10 + -12s + 2s2 = 10 + 2s + -10 + -2s

Reorder the terms:
-10 + -12s + 2s2 = 10 + -10 + 2s + -2s

Combine like terms: 10 + -10 = 0
-10 + -12s + 2s2 = 0 + 2s + -2s
-10 + -12s + 2s2 = 2s + -2s

Combine like terms: 2s + -2s = 0
-10 + -12s + 2s2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -6s + s2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -6s + s2)' equal to zero and attempt to solve:

Simplifying
-5 + -6s + s2 = 0

Solving
-5 + -6s + s2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -6s + 5 + s2 = 0 + 5

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

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

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

The s term is -6s.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6s + 9 + s2 = 5 + 9

Reorder the terms:
9 + -6s + s2 = 5 + 9

Combine like terms: 5 + 9 = 14
9 + -6s + s2 = 14

Factor a perfect square on the left side:
(s + -3)(s + -3) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(s + -3) equal to 3.741657387 and -3.741657387.

Subproblem 1
s + -3 = 3.741657387

Simplifying
s + -3 = 3.741657387

Reorder the terms:
-3 + s = 3.741657387

Solving
-3 + s = 3.741657387

Solving for variable 's'.

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

Add '3' to each side of the equation.
-3 + 3 + s = 3.741657387 + 3

Combine like terms: -3 + 3 = 0
0 + s = 3.741657387 + 3
s = 3.741657387 + 3

Combine like terms: 3.741657387 + 3 = 6.741657387
s = 6.741657387

Simplifying
s = 6.741657387

Subproblem 2
s + -3 = -3.741657387

Simplifying
s + -3 = -3.741657387

Reorder the terms:
-3 + s = -3.741657387

Solving
-3 + s = -3.741657387

Solving for variable 's'.

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

Add '3' to each side of the equation.
-3 + 3 + s = -3.741657387 + 3

Combine like terms: -3 + 3 = 0
0 + s = -3.741657387 + 3
s = -3.741657387 + 3

Combine like terms: -3.741657387 + 3 = -0.741657387
s = -0.741657387

Simplifying
s = -0.741657387

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {6.741657387, -0.741657387}
Solution
s = {6.741657387, -0.741657387}