(3p+1)(8p-3)=0

Solution for (3p+1)(8p-3)=0 equation:

Simplifying
(3p + 1)(8p + -3) = 0

Reorder the terms:
(1 + 3p)(8p + -3) = 0

Reorder the terms:
(1 + 3p)(-3 + 8p) = 0

Multiply (1 + 3p) * (-3 + 8p)
(1(-3 + 8p) + 3p * (-3 + 8p)) = 0
((-3 * 1 + 8p * 1) + 3p * (-3 + 8p)) = 0
((-3 + 8p) + 3p * (-3 + 8p)) = 0
(-3 + 8p + (-3 * 3p + 8p * 3p)) = 0
(-3 + 8p + (-9p + 24p2)) = 0

Combine like terms: 8p + -9p = -1p
(-3 + -1p + 24p2) = 0

Solving
-3 + -1p + 24p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-1 + -3p)(3 + -8p) = 0

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

Simplifying
-1 + -3p = 0

Solving
-1 + -3p = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3p = 0 + 1

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

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

Divide each side by '-3'.
p = -0.3333333333

Simplifying
p = -0.3333333333
Subproblem 2
Set the factor '(3 + -8p)' equal to zero and attempt to solve:

Simplifying
3 + -8p = 0

Solving
3 + -8p = 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 + -8p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8p = 0 + -3
-8p = 0 + -3

Combine like terms: 0 + -3 = -3
-8p = -3

Divide each side by '-8'.
p = 0.375

Simplifying
p = 0.375
Solution
p = {-0.3333333333, 0.375}