4(n^2-3-9)=-8n-36

Solution for 4(n^2-3-9)=-8n-36 equation:

Simplifying
4(n2 + -3 + -9) = -8n + -36

Reorder the terms:
4(-3 + -9 + n2) = -8n + -36

Combine like terms: -3 + -9 = -12
4(-12 + n2) = -8n + -36
(-12 * 4 + n2 * 4) = -8n + -36
(-48 + 4n2) = -8n + -36

Reorder the terms:
-48 + 4n2 = -36 + -8n

Solving
-48 + 4n2 = -36 + -8n

Solving for variable 'n'.

Reorder the terms:
-48 + 36 + 8n + 4n2 = -36 + -8n + 36 + 8n

Combine like terms: -48 + 36 = -12
-12 + 8n + 4n2 = -36 + -8n + 36 + 8n

Reorder the terms:
-12 + 8n + 4n2 = -36 + 36 + -8n + 8n

Combine like terms: -36 + 36 = 0
-12 + 8n + 4n2 = 0 + -8n + 8n
-12 + 8n + 4n2 = -8n + 8n

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

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

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

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
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
Solution
n = {-3, 1}