7n^2=28+21n

Solution for 7n^2=28+21n equation:

Simplifying
7n2 = 28 + 21n

Solving
7n2 = 28 + 21n

Solving for variable 'n'.

Reorder the terms:
-28 + -21n + 7n2 = 28 + 21n + -28 + -21n

Reorder the terms:
-28 + -21n + 7n2 = 28 + -28 + 21n + -21n

Combine like terms: 28 + -28 = 0
-28 + -21n + 7n2 = 0 + 21n + -21n
-28 + -21n + 7n2 = 21n + -21n

Combine like terms: 21n + -21n = 0
-28 + -21n + 7n2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-4 + -3n + n2) = 0

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

Ignore the factor 7.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-1, 4}