3p(2p-1)(p+4)=0

Solution for 3p(2p-1)(p+4)=0 equation:

Simplifying
3p(2p + -1)(p + 4) = 0

Reorder the terms:
3p(-1 + 2p)(p + 4) = 0

Reorder the terms:
3p(-1 + 2p)(4 + p) = 0

Multiply (-1 + 2p) * (4 + p)
3p(-1(4 + p) + 2p * (4 + p)) = 0
3p((4 * -1 + p * -1) + 2p * (4 + p)) = 0
3p((-4 + -1p) + 2p * (4 + p)) = 0
3p(-4 + -1p + (4 * 2p + p * 2p)) = 0
3p(-4 + -1p + (8p + 2p2)) = 0

Combine like terms: -1p + 8p = 7p
3p(-4 + 7p + 2p2) = 0
(-4 * 3p + 7p * 3p + 2p2 * 3p) = 0
(-12p + 21p2 + 6p3) = 0

Solving
-12p + 21p2 + 6p3 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3p'.
3p(-4 + 7p + 2p2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor 'p' equal to zero and attempt to solve:

Simplifying
p = 0

Solving
p = 0

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

Simplifying
p = 0
Subproblem 2
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 3
Set the factor '(1 + -2p)' equal to zero and attempt to solve:

Simplifying
1 + -2p = 0

Solving
1 + -2p = 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 + -2p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2p = 0 + -1
-2p = 0 + -1

Combine like terms: 0 + -1 = -1
-2p = -1

Divide each side by '-2'.
p = 0.5

Simplifying
p = 0.5
Solution
p = {0, -4, 0.5}