(s-4)(2s+1)=0

Solution for (s-4)(2s+1)=0 equation:

Simplifying
(s + -4)(2s + 1) = 0

Reorder the terms:
(-4 + s)(2s + 1) = 0

Reorder the terms:
(-4 + s)(1 + 2s) = 0

Multiply (-4 + s) * (1 + 2s)
(-4(1 + 2s) + s(1 + 2s)) = 0
((1 * -4 + 2s * -4) + s(1 + 2s)) = 0
((-4 + -8s) + s(1 + 2s)) = 0
(-4 + -8s + (1 * s + 2s * s)) = 0
(-4 + -8s + (1s + 2s2)) = 0

Combine like terms: -8s + 1s = -7s
(-4 + -7s + 2s2) = 0

Solving
-4 + -7s + 2s2 = 0

Solving for variable 's'.

Factor a trinomial.
(-1 + -2s)(4 + -1s) = 0

Subproblem 1
Set the factor '(-1 + -2s)' equal to zero and attempt to solve:

Simplifying
-1 + -2s = 0

Solving
-1 + -2s = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2s = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2s = 0 + 1
-2s = 0 + 1

Combine like terms: 0 + 1 = 1
-2s = 1

Divide each side by '-2'.
s = -0.5

Simplifying
s = -0.5
Subproblem 2
Set the factor '(4 + -1s)' equal to zero and attempt to solve:

Simplifying
4 + -1s = 0

Solving
4 + -1s = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1s = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1s = 0 + -4
-1s = 0 + -4

Combine like terms: 0 + -4 = -4
-1s = -4

Divide each side by '-1'.
s = 4

Simplifying
s = 4
Solution
s = {-0.5, 4}