(4n-2)(n-5)=0

Solution for (4n-2)(n-5)=0 equation:

Simplifying
(4n + -2)(n + -5) = 0

Reorder the terms:
(-2 + 4n)(n + -5) = 0

Reorder the terms:
(-2 + 4n)(-5 + n) = 0

Multiply (-2 + 4n) * (-5 + n)
(-2(-5 + n) + 4n * (-5 + n)) = 0
((-5 * -2 + n * -2) + 4n * (-5 + n)) = 0
((10 + -2n) + 4n * (-5 + n)) = 0
(10 + -2n + (-5 * 4n + n * 4n)) = 0
(10 + -2n + (-20n + 4n2)) = 0

Combine like terms: -2n + -20n = -22n
(10 + -22n + 4n2) = 0

Solving
10 + -22n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -11n + 2n2) = 0

Factor a trinomial.
2((1 + -2n)(5 + -1n)) = 0

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

Simplifying
1 + -2n = 0

Solving
1 + -2n = 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 + -2n = 0 + -1

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

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

Divide each side by '-2'.
n = 0.5

Simplifying
n = 0.5
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {0.5, 5}