(p+2)(6p-15)=0

Solution for (p+2)(6p-15)=0 equation:

Simplifying
(p + 2)(6p + -15) = 0

Reorder the terms:
(2 + p)(6p + -15) = 0

Reorder the terms:
(2 + p)(-15 + 6p) = 0

Multiply (2 + p) * (-15 + 6p)
(2(-15 + 6p) + p(-15 + 6p)) = 0
((-15 * 2 + 6p * 2) + p(-15 + 6p)) = 0
((-30 + 12p) + p(-15 + 6p)) = 0
(-30 + 12p + (-15 * p + 6p * p)) = 0
(-30 + 12p + (-15p + 6p2)) = 0

Combine like terms: 12p + -15p = -3p
(-30 + -3p + 6p2) = 0

Solving
-30 + -3p + 6p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -1p + 2p2) = 0

Factor a trinomial.
3((-2 + -1p)(5 + -2p)) = 0

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

Simplifying
-2 + -1p = 0

Solving
-2 + -1p = 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 + -1p = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1p = 0 + 2
-1p = 0 + 2

Combine like terms: 0 + 2 = 2
-1p = 2

Divide each side by '-1'.
p = -2

Simplifying
p = -2
Subproblem 2
Set the factor '(5 + -2p)' equal to zero and attempt to solve:

Simplifying
5 + -2p = 0

Solving
5 + -2p = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2p = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2p = 0 + -5
-2p = 0 + -5

Combine like terms: 0 + -5 = -5
-2p = -5

Divide each side by '-2'.
p = 2.5

Simplifying
p = 2.5
Solution
p = {-2, 2.5}