2p^2-3p-17=3

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

Simplifying
2p2 + -3p + -17 = 3

Reorder the terms:
-17 + -3p + 2p2 = 3

Solving
-17 + -3p + 2p2 = 3

Solving for variable 'p'.

Reorder the terms:
-17 + -3 + -3p + 2p2 = 3 + -3

Combine like terms: -17 + -3 = -20
-20 + -3p + 2p2 = 3 + -3

Combine like terms: 3 + -3 = 0
-20 + -3p + 2p2 = 0

Factor a trinomial.
(-5 + -2p)(4 + -1p) = 0

Subproblem 1
Set the factor '(-5 + -2p)' equal to zero and attempt to solve:

Simplifying
-5 + -2p = 0

Solving
-5 + -2p = 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 + -2p = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2p = 0 + 5
-2p = 0 + 5

Combine like terms: 0 + 5 = 5
-2p = 5

Divide each side by '-2'.
p = -2.5

Simplifying
p = -2.5
Subproblem 2
Set the factor '(4 + -1p)' equal to zero and attempt to solve:

Simplifying
4 + -1p = 0

Solving
4 + -1p = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1p = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1p = 0 + -4
-1p = 0 + -4

Combine like terms: 0 + -4 = -4
-1p = -4

Divide each side by '-1'.
p = 4

Simplifying
p = 4
Solution
p = {-2.5, 4}