8s(s+4)=s-21

Solution for 8s(s+4)=s-21 equation:

Simplifying
8s(s + 4) = s + -21

Reorder the terms:
8s(4 + s) = s + -21
(4 * 8s + s * 8s) = s + -21
(32s + 8s2) = s + -21

Reorder the terms:
32s + 8s2 = -21 + s

Solving
32s + 8s2 = -21 + s

Solving for variable 's'.

Reorder the terms:
21 + 32s + -1s + 8s2 = -21 + s + 21 + -1s

Combine like terms: 32s + -1s = 31s
21 + 31s + 8s2 = -21 + s + 21 + -1s

Reorder the terms:
21 + 31s + 8s2 = -21 + 21 + s + -1s

Combine like terms: -21 + 21 = 0
21 + 31s + 8s2 = 0 + s + -1s
21 + 31s + 8s2 = s + -1s

Combine like terms: s + -1s = 0
21 + 31s + 8s2 = 0

Factor a trinomial.
(3 + s)(7 + 8s) = 0

Subproblem 1
Set the factor '(3 + s)' equal to zero and attempt to solve:

Simplifying
3 + s = 0

Solving
3 + s = 0

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 = 0 + -3

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

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

Simplifying
s = -3
Subproblem 2
Set the factor '(7 + 8s)' equal to zero and attempt to solve:

Simplifying
7 + 8s = 0

Solving
7 + 8s = 0

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

Add '-7' to each side of the equation.
7 + -7 + 8s = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 8s = 0 + -7
8s = 0 + -7

Combine like terms: 0 + -7 = -7
8s = -7

Divide each side by '8'.
s = -0.875

Simplifying
s = -0.875
Solution
s = {-3, -0.875}