2p(p+5)-3(p+5)=

Solution for 2p(p+5)-3(p+5)= equation:

Simplifying
2p(p + 5) + -3(p + 5) = 0

Reorder the terms:
2p(5 + p) + -3(p + 5) = 0
(5 * 2p + p * 2p) + -3(p + 5) = 0
(10p + 2p2) + -3(p + 5) = 0

Reorder the terms:
10p + 2p2 + -3(5 + p) = 0
10p + 2p2 + (5 * -3 + p * -3) = 0
10p + 2p2 + (-15 + -3p) = 0

Reorder the terms:
-15 + 10p + -3p + 2p2 = 0

Combine like terms: 10p + -3p = 7p
-15 + 7p + 2p2 = 0

Solving
-15 + 7p + 2p2 = 0

Solving for variable 'p'.

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

Subproblem 1
Set the factor '(-5 + -1p)' equal to zero and attempt to solve:

Simplifying
-5 + -1p = 0

Solving
-5 + -1p = 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 + -1p = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1p = 0 + 5
-1p = 0 + 5

Combine like terms: 0 + 5 = 5
-1p = 5

Divide each side by '-1'.
p = -5

Simplifying
p = -5
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 = {-5, 1.5}