(4p-3)(2p+8)=0

Solution for (4p-3)(2p+8)=0 equation:

Simplifying
(4p + -3)(2p + 8) = 0

Reorder the terms:
(-3 + 4p)(2p + 8) = 0

Reorder the terms:
(-3 + 4p)(8 + 2p) = 0

Multiply (-3 + 4p) * (8 + 2p)
(-3(8 + 2p) + 4p * (8 + 2p)) = 0
((8 * -3 + 2p * -3) + 4p * (8 + 2p)) = 0
((-24 + -6p) + 4p * (8 + 2p)) = 0
(-24 + -6p + (8 * 4p + 2p * 4p)) = 0
(-24 + -6p + (32p + 8p2)) = 0

Combine like terms: -6p + 32p = 26p
(-24 + 26p + 8p2) = 0

Solving
-24 + 26p + 8p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 13p + 4p2) = 0

Factor a trinomial.
2((-4 + -1p)(3 + -4p)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -1p)' equal to zero and attempt to solve:

Simplifying
-4 + -1p = 0

Solving
-4 + -1p = 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 + -1p = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1p = 0 + 4
-1p = 0 + 4

Combine like terms: 0 + 4 = 4
-1p = 4

Divide each side by '-1'.
p = -4

Simplifying
p = -4
Subproblem 2
Set the factor '(3 + -4p)' equal to zero and attempt to solve:

Simplifying
3 + -4p = 0

Solving
3 + -4p = 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 + -4p = 0 + -3

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

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

Divide each side by '-4'.
p = 0.75

Simplifying
p = 0.75
Solution
p = {-4, 0.75}