(n-3)(3n+5)=0

Solution for (n-3)(3n+5)=0 equation:

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

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

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

Multiply (-3 + n) * (5 + 3n)
(-3(5 + 3n) + n(5 + 3n)) = 0
((5 * -3 + 3n * -3) + n(5 + 3n)) = 0
((-15 + -9n) + n(5 + 3n)) = 0
(-15 + -9n + (5 * n + 3n * n)) = 0
(-15 + -9n + (5n + 3n2)) = 0

Combine like terms: -9n + 5n = -4n
(-15 + -4n + 3n2) = 0

Solving
-15 + -4n + 3n2 = 0

Solving for variable 'n'.

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

Subproblem 1
Set the factor '(-5 + -3n)' equal to zero and attempt to solve:

Simplifying
-5 + -3n = 0

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

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

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

Divide each side by '-3'.
n = -1.666666667

Simplifying
n = -1.666666667
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 = {-1.666666667, 3}