3p^2=3p+6

Solution for 3p^2=3p+6 equation:

Simplifying
3p2 = 3p + 6

Reorder the terms:
3p2 = 6 + 3p

Solving
3p2 = 6 + 3p

Solving for variable 'p'.

Reorder the terms:
-6 + -3p + 3p2 = 6 + 3p + -6 + -3p

Reorder the terms:
-6 + -3p + 3p2 = 6 + -6 + 3p + -3p

Combine like terms: 6 + -6 = 0
-6 + -3p + 3p2 = 0 + 3p + -3p
-6 + -3p + 3p2 = 3p + -3p

Combine like terms: 3p + -3p = 0
-6 + -3p + 3p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -1p + p2) = 0

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

Ignore the factor 3.
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 '(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
Solution
p = {-1, 2}