(3p-4)(2p+5)=0

Solution for (3p-4)(2p+5)=0 equation:

Simplifying
(3p + -4)(2p + 5) = 0

Reorder the terms:
(-4 + 3p)(2p + 5) = 0

Reorder the terms:
(-4 + 3p)(5 + 2p) = 0

Multiply (-4 + 3p) * (5 + 2p)
(-4(5 + 2p) + 3p * (5 + 2p)) = 0
((5 * -4 + 2p * -4) + 3p * (5 + 2p)) = 0
((-20 + -8p) + 3p * (5 + 2p)) = 0
(-20 + -8p + (5 * 3p + 2p * 3p)) = 0
(-20 + -8p + (15p + 6p2)) = 0

Combine like terms: -8p + 15p = 7p
(-20 + 7p + 6p2) = 0

Solving
-20 + 7p + 6p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-5 + -2p)(4 + -3p) = 0

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

Simplifying
-5 + -2p = 0

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

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

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

Divide each side by '-2'.
p = -2.5

Simplifying
p = -2.5
Subproblem 2
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
Solution
p = {-2.5, 1.333333333}