4n^2+6n+2=870

Solution for 4n^2+6n+2=870 equation:

Simplifying
4n2 + 6n + 2 = 870

Reorder the terms:
2 + 6n + 4n2 = 870

Solving
2 + 6n + 4n2 = 870

Solving for variable 'n'.

Reorder the terms:
2 + -870 + 6n + 4n2 = 870 + -870

Combine like terms: 2 + -870 = -868
-868 + 6n + 4n2 = 870 + -870

Combine like terms: 870 + -870 = 0
-868 + 6n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-434 + 3n + 2n2) = 0

Factor a trinomial.
2((-31 + -2n)(14 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-31 + -2n)' equal to zero and attempt to solve:

Simplifying
-31 + -2n = 0

Solving
-31 + -2n = 0

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

Add '31' to each side of the equation.
-31 + 31 + -2n = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -2n = 0 + 31
-2n = 0 + 31

Combine like terms: 0 + 31 = 31
-2n = 31

Divide each side by '-2'.
n = -15.5

Simplifying
n = -15.5
Subproblem 2
Set the factor '(14 + -1n)' equal to zero and attempt to solve:

Simplifying
14 + -1n = 0

Solving
14 + -1n = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1n = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1n = 0 + -14
-1n = 0 + -14

Combine like terms: 0 + -14 = -14
-1n = -14

Divide each side by '-1'.
n = 14

Simplifying
n = 14
Solution
n = {-15.5, 14}