3=3+3n-5n^2

Solution for 3=3+3n-5n^2 equation:

Simplifying
3 = 3 + 3n + -5n2

Add '-3' to each side of the equation.
3 + -3 = 3 + 3n + -3 + -5n2

Combine like terms: 3 + -3 = 0
0 = 3 + 3n + -3 + -5n2

Reorder the terms:
0 = 3 + -3 + 3n + -5n2

Combine like terms: 3 + -3 = 0
0 = 0 + 3n + -5n2
0 = 3n + -5n2

Solving
0 = 3n + -5n2

Solving for variable 'n'.
Remove the zero:
-3n + 5n2 = 3n + -5n2 + -3n + 5n2

Reorder the terms:
-3n + 5n2 = 3n + -3n + -5n2 + 5n2

Combine like terms: 3n + -3n = 0
-3n + 5n2 = 0 + -5n2 + 5n2
-3n + 5n2 = -5n2 + 5n2

Combine like terms: -5n2 + 5n2 = 0
-3n + 5n2 = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-3 + 5n) = 0

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
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, 0.6}