12p^2+8p+1=0

Solution for 12p^2+8p+1=0 equation:

Simplifying
12p2 + 8p + 1 = 0

Reorder the terms:
1 + 8p + 12p2 = 0

Solving
1 + 8p + 12p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(1 + 2p)(1 + 6p) = 0

Subproblem 1
Set the factor '(1 + 2p)' equal to zero and attempt to solve:

Simplifying
1 + 2p = 0

Solving
1 + 2p = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2p = 0 + -1

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

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

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

Simplifying
p = -0.5
Subproblem 2
Set the factor '(1 + 6p)' equal to zero and attempt to solve:

Simplifying
1 + 6p = 0

Solving
1 + 6p = 0

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

Add '-1' to each side of the equation.
1 + -1 + 6p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6p = 0 + -1
6p = 0 + -1

Combine like terms: 0 + -1 = -1
6p = -1

Divide each side by '6'.
p = -0.1666666667

Simplifying
p = -0.1666666667
Solution
p = {-0.5, -0.1666666667}