7n^2+21=-52n

Solution for 7n^2+21=-52n equation:

Simplifying
7n2 + 21 = -52n

Reorder the terms:
21 + 7n2 = -52n

Solving
21 + 7n2 = -52n

Solving for variable 'n'.

Reorder the terms:
21 + 52n + 7n2 = -52n + 52n

Combine like terms: -52n + 52n = 0
21 + 52n + 7n2 = 0

Factor a trinomial.
(7 + n)(3 + 7n) = 0

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

Simplifying
7 + n = 0

Solving
7 + n = 0

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

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

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

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

Simplifying
n = -7
Subproblem 2
Set the factor '(3 + 7n)' equal to zero and attempt to solve:

Simplifying
3 + 7n = 0

Solving
3 + 7n = 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 + 7n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7n = 0 + -3
7n = 0 + -3

Combine like terms: 0 + -3 = -3
7n = -3

Divide each side by '7'.
n = -0.4285714286

Simplifying
n = -0.4285714286
Solution
n = {-7, -0.4285714286}