12n^2-21n+2=-8n+6

Solution for 12n^2-21n+2=-8n+6 equation:

Simplifying
12n2 + -21n + 2 = -8n + 6

Reorder the terms:
2 + -21n + 12n2 = -8n + 6

Reorder the terms:
2 + -21n + 12n2 = 6 + -8n

Solving
2 + -21n + 12n2 = 6 + -8n

Solving for variable 'n'.

Reorder the terms:
2 + -6 + -21n + 8n + 12n2 = 6 + -8n + -6 + 8n

Combine like terms: 2 + -6 = -4
-4 + -21n + 8n + 12n2 = 6 + -8n + -6 + 8n

Combine like terms: -21n + 8n = -13n
-4 + -13n + 12n2 = 6 + -8n + -6 + 8n

Reorder the terms:
-4 + -13n + 12n2 = 6 + -6 + -8n + 8n

Combine like terms: 6 + -6 = 0
-4 + -13n + 12n2 = 0 + -8n + 8n
-4 + -13n + 12n2 = -8n + 8n

Combine like terms: -8n + 8n = 0
-4 + -13n + 12n2 = 0

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

Subproblem 1
Set the factor '(-1 + -4n)' equal to zero and attempt to solve:

Simplifying
-1 + -4n = 0

Solving
-1 + -4n = 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 + -4n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4n = 0 + 1
-4n = 0 + 1

Combine like terms: 0 + 1 = 1
-4n = 1

Divide each side by '-4'.
n = -0.25

Simplifying
n = -0.25
Subproblem 2
Set the factor '(4 + -3n)' equal to zero and attempt to solve:

Simplifying
4 + -3n = 0

Solving
4 + -3n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3n = 0 + -4

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

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

Divide each side by '-3'.
n = 1.333333333

Simplifying
n = 1.333333333
Solution
n = {-0.25, 1.333333333}