4N^2+11N-3=0

Solution for 4N^2+11N-3=0 equation:

Simplifying
4N2 + 11N + -3 = 0

Reorder the terms:
-3 + 11N + 4N2 = 0

Solving
-3 + 11N + 4N2 = 0

Solving for variable 'N'.

Factor a trinomial.
(-3 + -1N)(1 + -4N) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + -4N)' equal to zero and attempt to solve:

Simplifying
1 + -4N = 0

Solving
1 + -4N = 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 + -4N = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4N = 0 + -1
-4N = 0 + -1

Combine like terms: 0 + -1 = -1
-4N = -1

Divide each side by '-4'.
N = 0.25

Simplifying
N = 0.25
Solution
N = {-3, 0.25}