4n^2-8n=21

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

Simplifying
4n2 + -8n = 21

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

Solving
-8n + 4n2 = 21

Solving for variable 'n'.

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

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

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

Subproblem 1
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
Subproblem 2
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
Solution
n = {-1.5, 3.5}