(4p)(3p-1)(p+12)=0

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Solution for (4p)(3p-1)(p+12)=0 equation: 


Simplifying
(4p)(3p + -1)(p + 12) = 0

Remove parenthesis around (4p)
4p(3p + -1)(p + 12) = 0

Reorder the terms:
4p(-1 + 3p)(p + 12) = 0

Reorder the terms:
4p(-1 + 3p)(12 + p) = 0

Multiply (-1 + 3p) * (12 + p)
4p(-1(12 + p) + 3p * (12 + p)) = 0
4p((12 * -1 + p * -1) + 3p * (12 + p)) = 0
4p((-12 + -1p) + 3p * (12 + p)) = 0
4p(-12 + -1p + (12 * 3p + p * 3p)) = 0
4p(-12 + -1p + (36p + 3p2)) = 0

Combine like terms: -1p + 36p = 35p
4p(-12 + 35p + 3p2) = 0
(-12 * 4p + 35p * 4p + 3p2 * 4p) = 0
(-48p + 140p2 + 12p3) = 0

Solving
-48p + 140p2 + 12p3 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '4p'.
4p(-12 + 35p + 3p2) = 0

Factor a trinomial.
4p((-12 + -1p)(1 + -3p)) = 0

Ignore the factor 4.

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 '(-12 + -1p)' equal to zero and attempt to solve:

Simplifying
-12 + -1p = 0

Solving
-12 + -1p = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1p = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1p = 0 + 12
-1p = 0 + 12

Combine like terms: 0 + 12 = 12
-1p = 12

Divide each side by '-1'.
p = -12

Simplifying
p = -12

Subproblem 3
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
Solution
p = {0, -12, 0.3333333333}

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