4n^2-2n-5=-3

Solution for 4n^2-2n-5=-3 equation:

Simplifying
4n2 + -2n + -5 = -3

Reorder the terms:
-5 + -2n + 4n2 = -3

Solving
-5 + -2n + 4n2 = -3

Solving for variable 'n'.

Reorder the terms:
-5 + 3 + -2n + 4n2 = -3 + 3

Combine like terms: -5 + 3 = -2
-2 + -2n + 4n2 = -3 + 3

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

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

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

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

Simplifying
-1 + -2n = 0

Solving
-1 + -2n = 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 + -2n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2n = 0 + 1
-2n = 0 + 1

Combine like terms: 0 + 1 = 1
-2n = 1

Divide each side by '-2'.
n = -0.5

Simplifying
n = -0.5
Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

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

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

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

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

Simplifying
n = 1
Solution
n = {-0.5, 1}