4n^2=21-8n

Solution for 4n^2=21-8n equation:

Simplifying
4n2 = 21 + -8n

Solving
4n2 = 21 + -8n

Solving for variable 'n'.

Reorder the terms:
-21 + 8n + 4n2 = 21 + -8n + -21 + 8n

Reorder the terms:
-21 + 8n + 4n2 = 21 + -21 + -8n + 8n

Combine like terms: 21 + -21 = 0
-21 + 8n + 4n2 = 0 + -8n + 8n
-21 + 8n + 4n2 = -8n + 8n

Combine like terms: -8n + 8n = 0
-21 + 8n + 4n2 = 0

Factor a trinomial.
(-7 + -2n)(3 + -2n) = 0

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

Simplifying
-7 + -2n = 0

Solving
-7 + -2n = 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 + -2n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2n = 0 + 7
-2n = 0 + 7

Combine like terms: 0 + 7 = 7
-2n = 7

Divide each side by '-2'.
n = -3.5

Simplifying
n = -3.5
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 = {-3.5, 1.5}