8n^2-8n=2n-3

Solution for 8n^2-8n=2n-3 equation:

Simplifying
8n2 + -8n = 2n + -3

Reorder the terms:
-8n + 8n2 = 2n + -3

Reorder the terms:
-8n + 8n2 = -3 + 2n

Solving
-8n + 8n2 = -3 + 2n

Solving for variable 'n'.

Reorder the terms:
3 + -8n + -2n + 8n2 = -3 + 2n + 3 + -2n

Combine like terms: -8n + -2n = -10n
3 + -10n + 8n2 = -3 + 2n + 3 + -2n

Reorder the terms:
3 + -10n + 8n2 = -3 + 3 + 2n + -2n

Combine like terms: -3 + 3 = 0
3 + -10n + 8n2 = 0 + 2n + -2n
3 + -10n + 8n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
3 + -10n + 8n2 = 0

Factor a trinomial.
(1 + -2n)(3 + -4n) = 0

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 '(3 + -4n)' equal to zero and attempt to solve:

Simplifying
3 + -4n = 0

Solving
3 + -4n = 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 + -4n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4n = 0 + -3
-4n = 0 + -3

Combine like terms: 0 + -3 = -3
-4n = -3

Divide each side by '-4'.
n = 0.75

Simplifying
n = 0.75
Solution
n = {0.5, 0.75}