(3n-4)(2n+3)=0

Solution for (3n-4)(2n+3)=0 equation:

Simplifying
(3n + -4)(2n + 3) = 0

Reorder the terms:
(-4 + 3n)(2n + 3) = 0

Reorder the terms:
(-4 + 3n)(3 + 2n) = 0

Multiply (-4 + 3n) * (3 + 2n)
(-4(3 + 2n) + 3n * (3 + 2n)) = 0
((3 * -4 + 2n * -4) + 3n * (3 + 2n)) = 0
((-12 + -8n) + 3n * (3 + 2n)) = 0
(-12 + -8n + (3 * 3n + 2n * 3n)) = 0
(-12 + -8n + (9n + 6n2)) = 0

Combine like terms: -8n + 9n = 1n
(-12 + 1n + 6n2) = 0

Solving
-12 + 1n + 6n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-3 + -2n)(4 + -3n) = 0

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

Simplifying
-3 + -2n = 0

Solving
-3 + -2n = 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 + -2n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2n = 0 + 3
-2n = 0 + 3

Combine like terms: 0 + 3 = 3
-2n = 3

Divide each side by '-2'.
n = -1.5

Simplifying
n = -1.5
Subproblem 2
Set the factor '(4 + -3n)' equal to zero and attempt to solve:

Simplifying
4 + -3n = 0

Solving
4 + -3n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3n = 0 + -4
-3n = 0 + -4

Combine like terms: 0 + -4 = -4
-3n = -4

Divide each side by '-3'.
n = 1.333333333

Simplifying
n = 1.333333333
Solution
n = {-1.5, 1.333333333}