(3p+4)(p-5)=0

Solution for (3p+4)(p-5)=0 equation:

Simplifying
(3p + 4)(p + -5) = 0

Reorder the terms:
(4 + 3p)(p + -5) = 0

Reorder the terms:
(4 + 3p)(-5 + p) = 0

Multiply (4 + 3p) * (-5 + p)
(4(-5 + p) + 3p * (-5 + p)) = 0
((-5 * 4 + p * 4) + 3p * (-5 + p)) = 0
((-20 + 4p) + 3p * (-5 + p)) = 0
(-20 + 4p + (-5 * 3p + p * 3p)) = 0
(-20 + 4p + (-15p + 3p2)) = 0

Combine like terms: 4p + -15p = -11p
(-20 + -11p + 3p2) = 0

Solving
-20 + -11p + 3p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-4 + -3p)(5 + -1p) = 0

Subproblem 1
Set the factor '(-4 + -3p)' equal to zero and attempt to solve:

Simplifying
-4 + -3p = 0

Solving
-4 + -3p = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3p = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3p = 0 + 4
-3p = 0 + 4

Combine like terms: 0 + 4 = 4
-3p = 4

Divide each side by '-3'.
p = -1.333333333

Simplifying
p = -1.333333333
Subproblem 2
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
Solution
p = {-1.333333333, 5}