3p^2=6-17p

Solution for 3p^2=6-17p equation:

Simplifying
3p2 = 6 + -17p

Solving
3p2 = 6 + -17p

Solving for variable 'p'.

Reorder the terms:
-6 + 17p + 3p2 = 6 + -17p + -6 + 17p

Reorder the terms:
-6 + 17p + 3p2 = 6 + -6 + -17p + 17p

Combine like terms: 6 + -6 = 0
-6 + 17p + 3p2 = 0 + -17p + 17p
-6 + 17p + 3p2 = -17p + 17p

Combine like terms: -17p + 17p = 0
-6 + 17p + 3p2 = 0

Factor a trinomial.
(-6 + -1p)(1 + -3p) = 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 '(1 + -3p)' equal to zero and attempt to solve:

Simplifying
1 + -3p = 0

Solving
1 + -3p = 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 + -3p = 0 + -1

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

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

Divide each side by '-3'.
p = 0.3333333333

Simplifying
p = 0.3333333333
Solution
p = {-6, 0.3333333333}