-10s(s+1)=21

Solution for -10s(s+1)=21 equation:

Simplifying
-10s(s + 1) = 21

Reorder the terms:
-10s(1 + s) = 21
(1 * -10s + s * -10s) = 21
(-10s + -10s2) = 21

Solving
-10s + -10s2 = 21

Solving for variable 's'.

Reorder the terms:
-21 + -10s + -10s2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + -10s + -10s2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(21 + 10s + 10s2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(21 + 10s + 10s2)' equal to zero and attempt to solve:

Simplifying
21 + 10s + 10s2 = 0

Solving
21 + 10s + 10s2 = 0

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

Divide each side by '10'.
2.1 + s + s2 = 0.0

Move the constant term to the right:

Add '-2.1' to each side of the equation.
2.1 + s + -2.1 + s2 = 0.0 + -2.1

Reorder the terms:
2.1 + -2.1 + s + s2 = 0.0 + -2.1

Combine like terms: 2.1 + -2.1 = 0.0
0.0 + s + s2 = 0.0 + -2.1
s + s2 = 0.0 + -2.1

Combine like terms: 0.0 + -2.1 = -2.1
s + s2 = -2.1

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

Add '0.25' to each side of the equation.
 + 0.25 + s2 = -2.1 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + s2 = -2.1 + 0.25

Combine like terms: -2.1 + 0.25 = -1.85
1.25 + s2 = -1.85

Factor a perfect square on the left side:
(s + 0.5)(s + 0.5) = -1.85

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.