3p(p+5)(4p+1)=

Solution for 3p(p+5)(4p+1)= equation:

Simplifying
3p(p + 5)(4p + 1) = 0

Reorder the terms:
3p(5 + p)(4p + 1) = 0

Reorder the terms:
3p(5 + p)(1 + 4p) = 0

Multiply (5 + p) * (1 + 4p)
3p(5(1 + 4p) + p(1 + 4p)) = 0
3p((1 * 5 + 4p * 5) + p(1 + 4p)) = 0
3p((5 + 20p) + p(1 + 4p)) = 0
3p(5 + 20p + (1 * p + 4p * p)) = 0
3p(5 + 20p + (1p + 4p2)) = 0

Combine like terms: 20p + 1p = 21p
3p(5 + 21p + 4p2) = 0
(5 * 3p + 21p * 3p + 4p2 * 3p) = 0
(15p + 63p2 + 12p3) = 0

Solving
15p + 63p2 + 12p3 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3p'.
3p(5 + 21p + 4p2) = 0

Factor a trinomial.
3p((5 + p)(1 + 4p)) = 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 '(5 + p)' equal to zero and attempt to solve:

Simplifying
5 + p = 0

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

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

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

Simplifying
p = -5
Subproblem 3
Set the factor '(1 + 4p)' equal to zero and attempt to solve:

Simplifying
1 + 4p = 0

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

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

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

Divide each side by '4'.
p = -0.25

Simplifying
p = -0.25
Solution
p = {0, -5, -0.25}