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

Solution for (5p+2)(3-2p)=0 equation:

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

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

Multiply (2 + 5p) * (3 + -2p)
(2(3 + -2p) + 5p * (3 + -2p)) = 0
((3 * 2 + -2p * 2) + 5p * (3 + -2p)) = 0
((6 + -4p) + 5p * (3 + -2p)) = 0
(6 + -4p + (3 * 5p + -2p * 5p)) = 0
(6 + -4p + (15p + -10p2)) = 0

Combine like terms: -4p + 15p = 11p
(6 + 11p + -10p2) = 0

Solving
6 + 11p + -10p2 = 0

Solving for variable 'p'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(2 + 5p)' equal to zero and attempt to solve:

Simplifying
2 + 5p = 0

Solving
2 + 5p = 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 + 5p = 0 + -2

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

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

Divide each side by '5'.
p = -0.4

Simplifying
p = -0.4
Solution
p = {1.5, -0.4}