(p-6)(3p-14)=0

Solution for (p-6)(3p-14)=0 equation:

Simplifying
(p + -6)(3p + -14) = 0

Reorder the terms:
(-6 + p)(3p + -14) = 0

Reorder the terms:
(-6 + p)(-14 + 3p) = 0

Multiply (-6 + p) * (-14 + 3p)
(-6(-14 + 3p) + p(-14 + 3p)) = 0
((-14 * -6 + 3p * -6) + p(-14 + 3p)) = 0
((84 + -18p) + p(-14 + 3p)) = 0
(84 + -18p + (-14 * p + 3p * p)) = 0
(84 + -18p + (-14p + 3p2)) = 0

Combine like terms: -18p + -14p = -32p
(84 + -32p + 3p2) = 0

Solving
84 + -32p + 3p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(14 + -3p)(6 + -1p) = 0

Subproblem 1
Set the factor '(14 + -3p)' equal to zero and attempt to solve:

Simplifying
14 + -3p = 0

Solving
14 + -3p = 0

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

Add '-14' to each side of the equation.
14 + -14 + -3p = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -3p = 0 + -14
-3p = 0 + -14

Combine like terms: 0 + -14 = -14
-3p = -14

Divide each side by '-3'.
p = 4.666666667

Simplifying
p = 4.666666667
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 = {4.666666667, 6}