40n^2+2n=24

Solution for 40n^2+2n=24 equation:

Simplifying
40n2 + 2n = 24

Reorder the terms:
2n + 40n2 = 24

Solving
2n + 40n2 = 24

Solving for variable 'n'.

Reorder the terms:
-24 + 2n + 40n2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 2n + 40n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + n + 20n2) = 0

Factor a trinomial.
2((-4 + -5n)(3 + -4n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -5n)' equal to zero and attempt to solve:

Simplifying
-4 + -5n = 0

Solving
-4 + -5n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -5n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5n = 0 + 4
-5n = 0 + 4

Combine like terms: 0 + 4 = 4
-5n = 4

Divide each side by '-5'.
n = -0.8

Simplifying
n = -0.8
Subproblem 2
Set the factor '(3 + -4n)' equal to zero and attempt to solve:

Simplifying
3 + -4n = 0

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

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

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

Divide each side by '-4'.
n = 0.75

Simplifying
n = 0.75
Solution
n = {-0.8, 0.75}