2n^2+28n=30

Solution for 2n^2+28n=30 equation:

Simplifying
2n2 + 28n = 30

Reorder the terms:
28n + 2n2 = 30

Solving
28n + 2n2 = 30

Solving for variable 'n'.

Reorder the terms:
-30 + 28n + 2n2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 28n + 2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 14n + n2) = 0

Factor a trinomial.
2((-15 + -1n)(1 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-15 + -1n)' equal to zero and attempt to solve:

Simplifying
-15 + -1n = 0

Solving
-15 + -1n = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1n = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1n = 0 + 15
-1n = 0 + 15

Combine like terms: 0 + 15 = 15
-1n = 15

Divide each side by '-1'.
n = -15

Simplifying
n = -15
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 = {-15, 1}