21p^2+186p+144=0

Solution for 21p^2+186p+144=0 equation:

Simplifying
21p2 + 186p + 144 = 0

Reorder the terms:
144 + 186p + 21p2 = 0

Solving
144 + 186p + 21p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3'.
3(48 + 62p + 7p2) = 0

Factor a trinomial.
3((8 + p)(6 + 7p)) = 0

Ignore the factor 3.
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 '(6 + 7p)' equal to zero and attempt to solve:

Simplifying
6 + 7p = 0

Solving
6 + 7p = 0

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

Add '-6' to each side of the equation.
6 + -6 + 7p = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7p = 0 + -6
7p = 0 + -6

Combine like terms: 0 + -6 = -6
7p = -6

Divide each side by '7'.
p = -0.8571428571

Simplifying
p = -0.8571428571
Solution
p = {-8, -0.8571428571}