4n^2-32=28n

Solution for 4n^2-32=28n equation:

Simplifying
4n2 + -32 = 28n

Reorder the terms:
-32 + 4n2 = 28n

Solving
-32 + 4n2 = 28n

Solving for variable 'n'.

Reorder the terms:
-32 + -28n + 4n2 = 28n + -28n

Combine like terms: 28n + -28n = 0
-32 + -28n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-8 + -7n + n2) = 0

Factor a trinomial.
4((-1 + -1n)(8 + -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 '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {-1, 8}