(2s-9)(8s+1)=0

Solution for (2s-9)(8s+1)=0 equation:

Simplifying
(2s + -9)(8s + 1) = 0

Reorder the terms:
(-9 + 2s)(8s + 1) = 0

Reorder the terms:
(-9 + 2s)(1 + 8s) = 0

Multiply (-9 + 2s) * (1 + 8s)
(-9(1 + 8s) + 2s * (1 + 8s)) = 0
((1 * -9 + 8s * -9) + 2s * (1 + 8s)) = 0
((-9 + -72s) + 2s * (1 + 8s)) = 0
(-9 + -72s + (1 * 2s + 8s * 2s)) = 0
(-9 + -72s + (2s + 16s2)) = 0

Combine like terms: -72s + 2s = -70s
(-9 + -70s + 16s2) = 0

Solving
-9 + -70s + 16s2 = 0

Solving for variable 's'.

Factor a trinomial.
(-1 + -8s)(9 + -2s) = 0

Subproblem 1
Set the factor '(-1 + -8s)' equal to zero and attempt to solve:

Simplifying
-1 + -8s = 0

Solving
-1 + -8s = 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 + -8s = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8s = 0 + 1
-8s = 0 + 1

Combine like terms: 0 + 1 = 1
-8s = 1

Divide each side by '-8'.
s = -0.125

Simplifying
s = -0.125
Subproblem 2
Set the factor '(9 + -2s)' equal to zero and attempt to solve:

Simplifying
9 + -2s = 0

Solving
9 + -2s = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2s = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2s = 0 + -9
-2s = 0 + -9

Combine like terms: 0 + -9 = -9
-2s = -9

Divide each side by '-2'.
s = 4.5

Simplifying
s = 4.5
Solution
s = {-0.125, 4.5}