(4s-2)(5s-4)=0

Solution for (4s-2)(5s-4)=0 equation:

Simplifying
(4s + -2)(5s + -4) = 0

Reorder the terms:
(-2 + 4s)(5s + -4) = 0

Reorder the terms:
(-2 + 4s)(-4 + 5s) = 0

Multiply (-2 + 4s) * (-4 + 5s)
(-2(-4 + 5s) + 4s * (-4 + 5s)) = 0
((-4 * -2 + 5s * -2) + 4s * (-4 + 5s)) = 0
((8 + -10s) + 4s * (-4 + 5s)) = 0
(8 + -10s + (-4 * 4s + 5s * 4s)) = 0
(8 + -10s + (-16s + 20s2)) = 0

Combine like terms: -10s + -16s = -26s
(8 + -26s + 20s2) = 0

Solving
8 + -26s + 20s2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -13s + 10s2) = 0

Factor a trinomial.
2((1 + -2s)(4 + -5s)) = 0

Ignore the factor 2.
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 + -5s)' equal to zero and attempt to solve:

Simplifying
4 + -5s = 0

Solving
4 + -5s = 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 + -5s = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5s = 0 + -4
-5s = 0 + -4

Combine like terms: 0 + -4 = -4
-5s = -4

Divide each side by '-5'.
s = 0.8

Simplifying
s = 0.8
Solution
s = {0.5, 0.8}