8n^2+32n+12=3n^2

Solution for 8n^2+32n+12=3n^2 equation:

Simplifying
8n2 + 32n + 12 = 3n2

Reorder the terms:
12 + 32n + 8n2 = 3n2

Solving
12 + 32n + 8n2 = 3n2

Solving for variable 'n'.

Combine like terms: 8n2 + -3n2 = 5n2
12 + 32n + 5n2 = 3n2 + -3n2

Combine like terms: 3n2 + -3n2 = 0
12 + 32n + 5n2 = 0

Factor a trinomial.
(6 + n)(2 + 5n) = 0

Subproblem 1
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 0

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

Add '-6' to each side of the equation.
6 + -6 + n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + n = 0 + -6
n = 0 + -6

Combine like terms: 0 + -6 = -6
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(2 + 5n)' equal to zero and attempt to solve:

Simplifying
2 + 5n = 0

Solving
2 + 5n = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5n = 0 + -2
5n = 0 + -2

Combine like terms: 0 + -2 = -2
5n = -2

Divide each side by '5'.
n = -0.4

Simplifying
n = -0.4
Solution
n = {-6, -0.4}