3p^2+6p=45

Solution for 3p^2+6p=45 equation:

Simplifying
3p2 + 6p = 45

Reorder the terms:
6p + 3p2 = 45

Solving
6p + 3p2 = 45

Solving for variable 'p'.

Reorder the terms:
-45 + 6p + 3p2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + 6p + 3p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 2p + p2) = 0

Factor a trinomial.
3((-5 + -1p)(3 + -1p)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -1p)' equal to zero and attempt to solve:

Simplifying
-5 + -1p = 0

Solving
-5 + -1p = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1p = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1p = 0 + 5
-1p = 0 + 5

Combine like terms: 0 + 5 = 5
-1p = 5

Divide each side by '-1'.
p = -5

Simplifying
p = -5
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 = {-5, 3}