(8n-3)(n-9)=0

Solution for (8n-3)(n-9)=0 equation:

Simplifying
(8n + -3)(n + -9) = 0

Reorder the terms:
(-3 + 8n)(n + -9) = 0

Reorder the terms:
(-3 + 8n)(-9 + n) = 0

Multiply (-3 + 8n) * (-9 + n)
(-3(-9 + n) + 8n * (-9 + n)) = 0
((-9 * -3 + n * -3) + 8n * (-9 + n)) = 0
((27 + -3n) + 8n * (-9 + n)) = 0
(27 + -3n + (-9 * 8n + n * 8n)) = 0
(27 + -3n + (-72n + 8n2)) = 0

Combine like terms: -3n + -72n = -75n
(27 + -75n + 8n2) = 0

Solving
27 + -75n + 8n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(3 + -8n)(9 + -1n) = 0

Subproblem 1
Set the factor '(3 + -8n)' equal to zero and attempt to solve:

Simplifying
3 + -8n = 0

Solving
3 + -8n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -8n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8n = 0 + -3
-8n = 0 + -3

Combine like terms: 0 + -3 = -3
-8n = -3

Divide each side by '-8'.
n = 0.375

Simplifying
n = 0.375
Subproblem 2
Set the factor '(9 + -1n)' equal to zero and attempt to solve:

Simplifying
9 + -1n = 0

Solving
9 + -1n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1n = 0 + -9
-1n = 0 + -9

Combine like terms: 0 + -9 = -9
-1n = -9

Divide each side by '-1'.
n = 9

Simplifying
n = 9
Solution
n = {0.375, 9}