28n^2+68n=-40

Solution for 28n^2+68n=-40 equation:

Simplifying
28n2 + 68n = -40

Reorder the terms:
68n + 28n2 = -40

Solving
68n + 28n2 = -40

Solving for variable 'n'.

Reorder the terms:
40 + 68n + 28n2 = -40 + 40

Combine like terms: -40 + 40 = 0
40 + 68n + 28n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(10 + 17n + 7n2) = 0

Factor a trinomial.
4((10 + 7n)(1 + n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(10 + 7n)' equal to zero and attempt to solve:

Simplifying
10 + 7n = 0

Solving
10 + 7n = 0

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

Add '-10' to each side of the equation.
10 + -10 + 7n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 7n = 0 + -10
7n = 0 + -10

Combine like terms: 0 + -10 = -10
7n = -10

Divide each side by '7'.
n = -1.428571429

Simplifying
n = -1.428571429
Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

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

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

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

Simplifying
n = -1
Solution
n = {-1.428571429, -1}