9p^2=-21p-6

Solution for 9p^2=-21p-6 equation:

Simplifying
9p2 = -21p + -6

Reorder the terms:
9p2 = -6 + -21p

Solving
9p2 = -6 + -21p

Solving for variable 'p'.

Reorder the terms:
6 + 21p + 9p2 = -6 + -21p + 6 + 21p

Reorder the terms:
6 + 21p + 9p2 = -6 + 6 + -21p + 21p

Combine like terms: -6 + 6 = 0
6 + 21p + 9p2 = 0 + -21p + 21p
6 + 21p + 9p2 = -21p + 21p

Combine like terms: -21p + 21p = 0
6 + 21p + 9p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + 7p + 3p2) = 0

Factor a trinomial.
3((2 + p)(1 + 3p)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + p)' equal to zero and attempt to solve:

Simplifying
2 + p = 0

Solving
2 + p = 0

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

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

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

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

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

Simplifying
1 + 3p = 0

Solving
1 + 3p = 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 + 3p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3p = 0 + -1
3p = 0 + -1

Combine like terms: 0 + -1 = -1
3p = -1

Divide each side by '3'.
p = -0.3333333333

Simplifying
p = -0.3333333333
Solution
p = {-2, -0.3333333333}