(4n-2)(5n-3)=

Solution for (4n-2)(5n-3)= equation:

Simplifying
(4n + -2)(5n + -3) = 0

Reorder the terms:
(-2 + 4n)(5n + -3) = 0

Reorder the terms:
(-2 + 4n)(-3 + 5n) = 0

Multiply (-2 + 4n) * (-3 + 5n)
(-2(-3 + 5n) + 4n * (-3 + 5n)) = 0
((-3 * -2 + 5n * -2) + 4n * (-3 + 5n)) = 0
((6 + -10n) + 4n * (-3 + 5n)) = 0
(6 + -10n + (-3 * 4n + 5n * 4n)) = 0
(6 + -10n + (-12n + 20n2)) = 0

Combine like terms: -10n + -12n = -22n
(6 + -22n + 20n2) = 0

Solving
6 + -22n + 20n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -11n + 10n2) = 0

Factor a trinomial.
2((1 + -2n)(3 + -5n)) = 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 '(3 + -5n)' equal to zero and attempt to solve:

Simplifying
3 + -5n = 0

Solving
3 + -5n = 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 + -5n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5n = 0 + -3
-5n = 0 + -3

Combine like terms: 0 + -3 = -3
-5n = -3

Divide each side by '-5'.
n = 0.6

Simplifying
n = 0.6
Solution
n = {0.5, 0.6}