12p^2+99p+51=3-3p

Solution for 12p^2+99p+51=3-3p equation:

Simplifying
12p2 + 99p + 51 = 3 + -3p

Reorder the terms:
51 + 99p + 12p2 = 3 + -3p

Solving
51 + 99p + 12p2 = 3 + -3p

Solving for variable 'p'.

Reorder the terms:
51 + -3 + 99p + 3p + 12p2 = 3 + -3p + -3 + 3p

Combine like terms: 51 + -3 = 48
48 + 99p + 3p + 12p2 = 3 + -3p + -3 + 3p

Combine like terms: 99p + 3p = 102p
48 + 102p + 12p2 = 3 + -3p + -3 + 3p

Reorder the terms:
48 + 102p + 12p2 = 3 + -3 + -3p + 3p

Combine like terms: 3 + -3 = 0
48 + 102p + 12p2 = 0 + -3p + 3p
48 + 102p + 12p2 = -3p + 3p

Combine like terms: -3p + 3p = 0
48 + 102p + 12p2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(8 + 17p + 2p2) = 0

Factor a trinomial.
6((8 + p)(1 + 2p)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(8 + p)' equal to zero and attempt to solve:

Simplifying
8 + p = 0

Solving
8 + p = 0

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

Add '-8' to each side of the equation.
8 + -8 + p = 0 + -8

Combine like terms: 8 + -8 = 0
0 + p = 0 + -8
p = 0 + -8

Combine like terms: 0 + -8 = -8
p = -8

Simplifying
p = -8
Subproblem 2
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
Solution
p = {-8, -0.5}