(3p-7)(p+6)=

Solution for (3p-7)(p+6)= equation:

Simplifying
(3p + -7)(p + 6) = 0

Reorder the terms:
(-7 + 3p)(p + 6) = 0

Reorder the terms:
(-7 + 3p)(6 + p) = 0

Multiply (-7 + 3p) * (6 + p)
(-7(6 + p) + 3p * (6 + p)) = 0
((6 * -7 + p * -7) + 3p * (6 + p)) = 0
((-42 + -7p) + 3p * (6 + p)) = 0
(-42 + -7p + (6 * 3p + p * 3p)) = 0
(-42 + -7p + (18p + 3p2)) = 0

Combine like terms: -7p + 18p = 11p
(-42 + 11p + 3p2) = 0

Solving
-42 + 11p + 3p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-6 + -1p)(7 + -3p) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -3p)' equal to zero and attempt to solve:

Simplifying
7 + -3p = 0

Solving
7 + -3p = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3p = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3p = 0 + -7
-3p = 0 + -7

Combine like terms: 0 + -7 = -7
-3p = -7

Divide each side by '-3'.
p = 2.333333333

Simplifying
p = 2.333333333
Solution
p = {-6, 2.333333333}