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

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

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

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

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

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

Combine like terms: -15p + 2p = -13p
(-6 + -13p + 5p2) = 0

Solving
-6 + -13p + 5p2 = 0

Solving for variable 'p'.

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

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

Simplifying
3 + -1p = 0

Solving
3 + -1p = 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 + -1p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1p = 0 + -3
-1p = 0 + -3

Combine like terms: 0 + -3 = -3
-1p = -3

Divide each side by '-1'.
p = 3

Simplifying
p = 3
Solution
p = {-0.4, 3}