(4s-1)(5s+3)=0

Solution for (4s-1)(5s+3)=0 equation:

Simplifying
(4s + -1)(5s + 3) = 0

Reorder the terms:
(-1 + 4s)(5s + 3) = 0

Reorder the terms:
(-1 + 4s)(3 + 5s) = 0

Multiply (-1 + 4s) * (3 + 5s)
(-1(3 + 5s) + 4s * (3 + 5s)) = 0
((3 * -1 + 5s * -1) + 4s * (3 + 5s)) = 0
((-3 + -5s) + 4s * (3 + 5s)) = 0
(-3 + -5s + (3 * 4s + 5s * 4s)) = 0
(-3 + -5s + (12s + 20s2)) = 0

Combine like terms: -5s + 12s = 7s
(-3 + 7s + 20s2) = 0

Solving
-3 + 7s + 20s2 = 0

Solving for variable 's'.

Factor a trinomial.
(-3 + -5s)(1 + -4s) = 0

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

Simplifying
-3 + -5s = 0

Solving
-3 + -5s = 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 + -5s = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5s = 0 + 3
-5s = 0 + 3

Combine like terms: 0 + 3 = 3
-5s = 3

Divide each side by '-5'.
s = -0.6

Simplifying
s = -0.6
Subproblem 2
Set the factor '(1 + -4s)' equal to zero and attempt to solve:

Simplifying
1 + -4s = 0

Solving
1 + -4s = 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 + -4s = 0 + -1

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

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

Divide each side by '-4'.
s = 0.25

Simplifying
s = 0.25
Solution
s = {-0.6, 0.25}