14n^2=7n+21

Solution for 14n^2=7n+21 equation:

Simplifying
14n2 = 7n + 21

Reorder the terms:
14n2 = 21 + 7n

Solving
14n2 = 21 + 7n

Solving for variable 'n'.

Reorder the terms:
-21 + -7n + 14n2 = 21 + 7n + -21 + -7n

Reorder the terms:
-21 + -7n + 14n2 = 21 + -21 + 7n + -7n

Combine like terms: 21 + -21 = 0
-21 + -7n + 14n2 = 0 + 7n + -7n
-21 + -7n + 14n2 = 7n + -7n

Combine like terms: 7n + -7n = 0
-21 + -7n + 14n2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-3 + -1n + 2n2) = 0

Factor a trinomial.
7((-1 + -1n)(3 + -2n)) = 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 '(3 + -2n)' equal to zero and attempt to solve:

Simplifying
3 + -2n = 0

Solving
3 + -2n = 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 + -2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2n = 0 + -3
-2n = 0 + -3

Combine like terms: 0 + -3 = -3
-2n = -3

Divide each side by '-2'.
n = 1.5

Simplifying
n = 1.5
Solution
n = {-1, 1.5}