30n^2-4n+1=3

Solution for 30n^2-4n+1=3 equation:

Simplifying
30n2 + -4n + 1 = 3

Reorder the terms:
1 + -4n + 30n2 = 3

Solving
1 + -4n + 30n2 = 3

Solving for variable 'n'.

Reorder the terms:
1 + -3 + -4n + 30n2 = 3 + -3

Combine like terms: 1 + -3 = -2
-2 + -4n + 30n2 = 3 + -3

Combine like terms: 3 + -3 = 0
-2 + -4n + 30n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -2n + 15n2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -5n)' equal to zero and attempt to solve:

Simplifying
-1 + -5n = 0

Solving
-1 + -5n = 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 + -5n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5n = 0 + 1
-5n = 0 + 1

Combine like terms: 0 + 1 = 1
-5n = 1

Divide each side by '-5'.
n = -0.2

Simplifying
n = -0.2
Subproblem 2
Set the factor '(1 + -3n)' equal to zero and attempt to solve:

Simplifying
1 + -3n = 0

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

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

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

Divide each side by '-3'.
n = 0.3333333333

Simplifying
n = 0.3333333333
Solution
n = {-0.2, 0.3333333333}