3p^2+17p=-10

Solution for 3p^2+17p=-10 equation:

Simplifying
3p2 + 17p = -10

Reorder the terms:
17p + 3p2 = -10

Solving
17p + 3p2 = -10

Solving for variable 'p'.

Reorder the terms:
10 + 17p + 3p2 = -10 + 10

Combine like terms: -10 + 10 = 0
10 + 17p + 3p2 = 0

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

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

Simplifying
5 + p = 0

Solving
5 + p = 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 + p = 0 + -5

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

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

Simplifying
p = -5
Subproblem 2
Set the factor '(2 + 3p)' equal to zero and attempt to solve:

Simplifying
2 + 3p = 0

Solving
2 + 3p = 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 + 3p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3p = 0 + -2
3p = 0 + -2

Combine like terms: 0 + -2 = -2
3p = -2

Divide each side by '3'.
p = -0.6666666667

Simplifying
p = -0.6666666667
Solution
p = {-5, -0.6666666667}