p^2=18-3p

Solution for p^2=18-3p equation:

Simplifying
p2 = 18 + -3p

Solving
p2 = 18 + -3p

Solving for variable 'p'.

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

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

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

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

Factor a trinomial.
(-6 + -1p)(3 + -1p) = 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 '(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 = {-6, 3}