3p(p-1)=18

Solution for 3p(p-1)=18 equation:

Simplifying
3p(p + -1) = 18

Reorder the terms:
3p(-1 + p) = 18
(-1 * 3p + p * 3p) = 18
(-3p + 3p2) = 18

Solving
-3p + 3p2 = 18

Solving for variable 'p'.

Reorder the terms:
-18 + -3p + 3p2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + -3p + 3p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + -1p + p2) = 0

Factor a trinomial.
3((-2 + -1p)(3 + -1p)) = 0

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

Simplifying
-2 + -1p = 0

Solving
-2 + -1p = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1p = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1p = 0 + 2
-1p = 0 + 2

Combine like terms: 0 + 2 = 2
-1p = 2

Divide each side by '-1'.
p = -2

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

Simplifying
3 + -1p = 0

Solving
3 + -1p = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1p = 0 + -3
-1p = 0 + -3

Combine like terms: 0 + -3 = -3
-1p = -3

Divide each side by '-1'.
p = 3

Simplifying
p = 3
Solution
p = {-2, 3}