8n^2+2=8n

Solution for 8n^2+2=8n equation:

Simplifying
8n2 + 2 = 8n

Reorder the terms:
2 + 8n2 = 8n

Solving
2 + 8n2 = 8n

Solving for variable 'n'.

Reorder the terms:
2 + -8n + 8n2 = 8n + -8n

Combine like terms: 8n + -8n = 0
2 + -8n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -4n + 4n2) = 0

Factor a trinomial.
2((1 + -2n)(1 + -2n)) = 0

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

Simplifying
1 + -2n = 0

Solving
1 + -2n = 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 + -2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2n = 0 + -1
-2n = 0 + -1

Combine like terms: 0 + -1 = -1
-2n = -1

Divide each side by '-2'.
n = 0.5

Simplifying
n = 0.5
Subproblem 2
Set the factor '(1 + -2n)' equal to zero and attempt to solve:

Simplifying
1 + -2n = 0

Solving
1 + -2n = 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 + -2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2n = 0 + -1
-2n = 0 + -1

Combine like terms: 0 + -1 = -1
-2n = -1

Divide each side by '-2'.
n = 0.5

Simplifying
n = 0.5
Solution
n = {0.5, 0.5}