4n^2+62n=32

Solution for 4n^2+62n=32 equation:

Simplifying
4n2 + 62n = 32

Reorder the terms:
62n + 4n2 = 32

Solving
62n + 4n2 = 32

Solving for variable 'n'.

Reorder the terms:
-32 + 62n + 4n2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + 62n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 31n + 2n2) = 0

Factor a trinomial.
2((-16 + -1n)(1 + -2n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-16 + -1n)' equal to zero and attempt to solve:

Simplifying
-16 + -1n = 0

Solving
-16 + -1n = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1n = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1n = 0 + 16
-1n = 0 + 16

Combine like terms: 0 + 16 = 16
-1n = 16

Divide each side by '-1'.
n = -16

Simplifying
n = -16
Subproblem 2
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
Solution
n = {-16, 0.5}