(3p-11)(p+1)=0

Solution for (3p-11)(p+1)=0 equation:

Simplifying
(3p + -11)(p + 1) = 0

Reorder the terms:
(-11 + 3p)(p + 1) = 0

Reorder the terms:
(-11 + 3p)(1 + p) = 0

Multiply (-11 + 3p) * (1 + p)
(-11(1 + p) + 3p * (1 + p)) = 0
((1 * -11 + p * -11) + 3p * (1 + p)) = 0
((-11 + -11p) + 3p * (1 + p)) = 0
(-11 + -11p + (1 * 3p + p * 3p)) = 0
(-11 + -11p + (3p + 3p2)) = 0

Combine like terms: -11p + 3p = -8p
(-11 + -8p + 3p2) = 0

Solving
-11 + -8p + 3p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-1 + -1p)(11 + -3p) = 0

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

Simplifying
-1 + -1p = 0

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

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

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

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

Simplifying
p = -1
Subproblem 2
Set the factor '(11 + -3p)' equal to zero and attempt to solve:

Simplifying
11 + -3p = 0

Solving
11 + -3p = 0

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

Add '-11' to each side of the equation.
11 + -11 + -3p = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3p = 0 + -11
-3p = 0 + -11

Combine like terms: 0 + -11 = -11
-3p = -11

Divide each side by '-3'.
p = 3.666666667

Simplifying
p = 3.666666667
Solution
p = {-1, 3.666666667}