3p^2=-12p-9

Solution for 3p^2=-12p-9 equation:

Simplifying
3p2 = -12p + -9

Reorder the terms:
3p2 = -9 + -12p

Solving
3p2 = -9 + -12p

Solving for variable 'p'.

Reorder the terms:
9 + 12p + 3p2 = -9 + -12p + 9 + 12p

Reorder the terms:
9 + 12p + 3p2 = -9 + 9 + -12p + 12p

Combine like terms: -9 + 9 = 0
9 + 12p + 3p2 = 0 + -12p + 12p
9 + 12p + 3p2 = -12p + 12p

Combine like terms: -12p + 12p = 0
9 + 12p + 3p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 4p + p2) = 0

Factor a trinomial.
3((3 + p)(1 + p)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + p)' equal to zero and attempt to solve:

Simplifying
3 + p = 0

Solving
3 + p = 0

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

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

Combine like terms: 3 + -3 = 0
0 + p = 0 + -3
p = 0 + -3

Combine like terms: 0 + -3 = -3
p = -3

Simplifying
p = -3
Subproblem 2
Set the factor '(1 + p)' equal to zero and attempt to solve:

Simplifying
1 + p = 0

Solving
1 + p = 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 + p = 0 + -1

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

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

Simplifying
p = -1
Solution
p = {-3, -1}