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

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

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

Reorder the terms:
5n(-3 + n) = 2(n + -3)
(-3 * 5n + n * 5n) = 2(n + -3)
(-15n + 5n2) = 2(n + -3)

Reorder the terms:
-15n + 5n2 = 2(-3 + n)
-15n + 5n2 = (-3 * 2 + n * 2)
-15n + 5n2 = (-6 + 2n)

Solving
-15n + 5n2 = -6 + 2n

Solving for variable 'n'.

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

Combine like terms: -15n + -2n = -17n
6 + -17n + 5n2 = -6 + 2n + 6 + -2n

Reorder the terms:
6 + -17n + 5n2 = -6 + 6 + 2n + -2n

Combine like terms: -6 + 6 = 0
6 + -17n + 5n2 = 0 + 2n + -2n
6 + -17n + 5n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
6 + -17n + 5n2 = 0

Factor a trinomial.
(2 + -5n)(3 + -1n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 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 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {0.4, 3}