4n^2-8n-21=-9

Solution for 4n^2-8n-21=-9 equation:

Simplifying
4n2 + -8n + -21 = -9

Reorder the terms:
-21 + -8n + 4n2 = -9

Solving
-21 + -8n + 4n2 = -9

Solving for variable 'n'.

Reorder the terms:
-21 + 9 + -8n + 4n2 = -9 + 9

Combine like terms: -21 + 9 = -12
-12 + -8n + 4n2 = -9 + 9

Combine like terms: -9 + 9 = 0
-12 + -8n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + -2n + n2) = 0

Factor a trinomial.
4((-1 + -1n)(3 + -1n)) = 0

Ignore the factor 4.
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 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 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 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-1, 3}