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

Subproblem 1
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
Subproblem 2
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
Solution
n = {-1.333333333, 1.5}