(5n-2)3n-(5n-2)(n-1)=

Solution for (5n-2)3n-(5n-2)(n-1)= equation:

Simplifying
(5n + -2) * 3n + -1(5n + -2)(n + -1) = 0

Reorder the terms:
(-2 + 5n) * 3n + -1(5n + -2)(n + -1) = 0

Reorder the terms for easier multiplication:
3n(-2 + 5n) + -1(5n + -2)(n + -1) = 0
(-2 * 3n + 5n * 3n) + -1(5n + -2)(n + -1) = 0
(-6n + 15n2) + -1(5n + -2)(n + -1) = 0

Reorder the terms:
-6n + 15n2 + -1(-2 + 5n)(n + -1) = 0

Reorder the terms:
-6n + 15n2 + -1(-2 + 5n)(-1 + n) = 0

Multiply (-2 + 5n) * (-1 + n)
-6n + 15n2 + -1(-2(-1 + n) + 5n * (-1 + n)) = 0
-6n + 15n2 + -1((-1 * -2 + n * -2) + 5n * (-1 + n)) = 0
-6n + 15n2 + -1((2 + -2n) + 5n * (-1 + n)) = 0
-6n + 15n2 + -1(2 + -2n + (-1 * 5n + n * 5n)) = 0
-6n + 15n2 + -1(2 + -2n + (-5n + 5n2)) = 0

Combine like terms: -2n + -5n = -7n
-6n + 15n2 + -1(2 + -7n + 5n2) = 0
-6n + 15n2 + (2 * -1 + -7n * -1 + 5n2 * -1) = 0
-6n + 15n2 + (-2 + 7n + -5n2) = 0

Reorder the terms:
-2 + -6n + 7n + 15n2 + -5n2 = 0

Combine like terms: -6n + 7n = 1n
-2 + 1n + 15n2 + -5n2 = 0

Combine like terms: 15n2 + -5n2 = 10n2
-2 + 1n + 10n2 = 0

Solving
-2 + 1n + 10n2 = 0

Solving for variable 'n'.

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

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 '(2 + -5n)' equal to zero and attempt to solve:

Simplifying
2 + -5n = 0

Solving
2 + -5n = 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 + -5n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5n = 0 + -2
-5n = 0 + -2

Combine like terms: 0 + -2 = -2
-5n = -2

Divide each side by '-5'.
n = 0.4

Simplifying
n = 0.4
Solution
n = {-0.5, 0.4}