6p^2=-21p-18

Solution for 6p^2=-21p-18 equation:

Simplifying
6p2 = -21p + -18

Reorder the terms:
6p2 = -18 + -21p

Solving
6p2 = -18 + -21p

Solving for variable 'p'.

Reorder the terms:
18 + 21p + 6p2 = -18 + -21p + 18 + 21p

Reorder the terms:
18 + 21p + 6p2 = -18 + 18 + -21p + 21p

Combine like terms: -18 + 18 = 0
18 + 21p + 6p2 = 0 + -21p + 21p
18 + 21p + 6p2 = -21p + 21p

Combine like terms: -21p + 21p = 0
18 + 21p + 6p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + 7p + 2p2) = 0

Factor a trinomial.
3((2 + p)(3 + 2p)) = 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 '(3 + 2p)' equal to zero and attempt to solve:

Simplifying
3 + 2p = 0

Solving
3 + 2p = 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 + 2p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2p = 0 + -3
2p = 0 + -3

Combine like terms: 0 + -3 = -3
2p = -3

Divide each side by '2'.
p = -1.5

Simplifying
p = -1.5
Solution
p = {-2, -1.5}