(3p-1)(2p+6)=-6

Solution for (3p-1)(2p+6)=-6 equation:

Simplifying
(3p + -1)(2p + 6) = -6

Reorder the terms:
(-1 + 3p)(2p + 6) = -6

Reorder the terms:
(-1 + 3p)(6 + 2p) = -6

Multiply (-1 + 3p) * (6 + 2p)
(-1(6 + 2p) + 3p * (6 + 2p)) = -6
((6 * -1 + 2p * -1) + 3p * (6 + 2p)) = -6
((-6 + -2p) + 3p * (6 + 2p)) = -6
(-6 + -2p + (6 * 3p + 2p * 3p)) = -6
(-6 + -2p + (18p + 6p2)) = -6

Combine like terms: -2p + 18p = 16p
(-6 + 16p + 6p2) = -6

Add '6' to each side of the equation.
-6 + 16p + 6 + 6p2 = -6 + 6

Reorder the terms:
-6 + 6 + 16p + 6p2 = -6 + 6

Combine like terms: -6 + 6 = 0
0 + 16p + 6p2 = -6 + 6
16p + 6p2 = -6 + 6

Combine like terms: -6 + 6 = 0
16p + 6p2 = 0

Solving
16p + 6p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2p'.
2p(8 + 3p) = 0

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

Simplifying
p = 0

Solving
p = 0

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

Simplifying
p = 0
Subproblem 2
Set the factor '(8 + 3p)' equal to zero and attempt to solve:

Simplifying
8 + 3p = 0

Solving
8 + 3p = 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 + 3p = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3p = 0 + -8
3p = 0 + -8

Combine like terms: 0 + -8 = -8
3p = -8

Divide each side by '3'.
p = -2.666666667

Simplifying
p = -2.666666667
Solution
p = {0, -2.666666667}