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

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

Simplifying
(2p + 3r)(p + -6r) = 0

Multiply (2p + 3r) * (p + -6r)
(2p * (p + -6r) + 3r * (p + -6r)) = 0
((p * 2p + -6r * 2p) + 3r * (p + -6r)) = 0

Reorder the terms:
((-12pr + 2p2) + 3r * (p + -6r)) = 0
((-12pr + 2p2) + 3r * (p + -6r)) = 0
(-12pr + 2p2 + (p * 3r + -6r * 3r)) = 0
(-12pr + 2p2 + (3pr + -18r2)) = 0

Reorder the terms:
(-12pr + 3pr + 2p2 + -18r2) = 0

Combine like terms: -12pr + 3pr = -9pr
(-9pr + 2p2 + -18r2) = 0

Solving
-9pr + 2p2 + -18r2 = 0

Solving for variable 'p'.

Factor a trinomial.
(p + -6r)(2p + 3r) = 0

Subproblem 1
Set the factor '(p + -6r)' equal to zero and attempt to solve:

Simplifying
p + -6r = 0

Solving
p + -6r = 0

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

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

Combine like terms: -6r + 6r = 0
p + 0 = 0 + 6r
p = 0 + 6r
Remove the zero:
p = 6r

Simplifying
p = 6r
Subproblem 2
Set the factor '(2p + 3r)' equal to zero and attempt to solve:

Simplifying
2p + 3r = 0

Solving
2p + 3r = 0

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

Add '-3r' to each side of the equation.
2p + 3r + -3r = 0 + -3r

Combine like terms: 3r + -3r = 0
2p + 0 = 0 + -3r
2p = 0 + -3r
Remove the zero:
2p = -3r

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

Simplifying
p = -1.5r
Solution
p = {6r, -1.5r}