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

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

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

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

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

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

Combine like terms: -3n + -8n = -11n
(6 + -11n + 4n2) = 0

Solving
6 + -11n + 4n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(3 + -4n)(2 + -1n) = 0

Subproblem 1
Set the factor '(3 + -4n)' equal to zero and attempt to solve:

Simplifying
3 + -4n = 0

Solving
3 + -4n = 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 + -4n = 0 + -3

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

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

Divide each side by '-4'.
n = 0.75

Simplifying
n = 0.75
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {0.75, 2}