(3p+4)(p-6)=0

Solution for (3p+4)(p-6)=0 equation:

Simplifying
(3p + 4)(p + -6) = 0

Reorder the terms:
(4 + 3p)(p + -6) = 0

Reorder the terms:
(4 + 3p)(-6 + p) = 0

Multiply (4 + 3p) * (-6 + p)
(4(-6 + p) + 3p * (-6 + p)) = 0
((-6 * 4 + p * 4) + 3p * (-6 + p)) = 0
((-24 + 4p) + 3p * (-6 + p)) = 0
(-24 + 4p + (-6 * 3p + p * 3p)) = 0
(-24 + 4p + (-18p + 3p2)) = 0

Combine like terms: 4p + -18p = -14p
(-24 + -14p + 3p2) = 0

Solving
-24 + -14p + 3p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-4 + -3p)(6 + -1p) = 0

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

Simplifying
-4 + -3p = 0

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

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

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

Divide each side by '-3'.
p = -1.333333333

Simplifying
p = -1.333333333
Subproblem 2
Set the factor '(6 + -1p)' equal to zero and attempt to solve:

Simplifying
6 + -1p = 0

Solving
6 + -1p = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1p = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1p = 0 + -6
-1p = 0 + -6

Combine like terms: 0 + -6 = -6
-1p = -6

Divide each side by '-1'.
p = 6

Simplifying
p = 6
Solution
p = {-1.333333333, 6}