(8n+2)(9n-3)=0

Solution for (8n+2)(9n-3)=0 equation:

Simplifying
(8n + 2)(9n + -3) = 0

Reorder the terms:
(2 + 8n)(9n + -3) = 0

Reorder the terms:
(2 + 8n)(-3 + 9n) = 0

Multiply (2 + 8n) * (-3 + 9n)
(2(-3 + 9n) + 8n * (-3 + 9n)) = 0
((-3 * 2 + 9n * 2) + 8n * (-3 + 9n)) = 0
((-6 + 18n) + 8n * (-3 + 9n)) = 0
(-6 + 18n + (-3 * 8n + 9n * 8n)) = 0
(-6 + 18n + (-24n + 72n2)) = 0

Combine like terms: 18n + -24n = -6n
(-6 + -6n + 72n2) = 0

Solving
-6 + -6n + 72n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + -1n + 12n2) = 0

Factor a trinomial.
6((-1 + -4n)(1 + -3n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + -4n)' equal to zero and attempt to solve:

Simplifying
-1 + -4n = 0

Solving
-1 + -4n = 0

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

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

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

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

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

Simplifying
n = -0.25
Subproblem 2
Set the factor '(1 + -3n)' equal to zero and attempt to solve:

Simplifying
1 + -3n = 0

Solving
1 + -3n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3n = 0 + -1
-3n = 0 + -1

Combine like terms: 0 + -1 = -1
-3n = -1

Divide each side by '-3'.
n = 0.3333333333

Simplifying
n = 0.3333333333
Solution
n = {-0.25, 0.3333333333}