4p^2+32p=17

Solution for 4p^2+32p=17 equation:

Simplifying
4p2 + 32p = 17

Reorder the terms:
32p + 4p2 = 17

Solving
32p + 4p2 = 17

Solving for variable 'p'.

Reorder the terms:
-17 + 32p + 4p2 = 17 + -17

Combine like terms: 17 + -17 = 0
-17 + 32p + 4p2 = 0

Factor a trinomial.
(-17 + -2p)(1 + -2p) = 0

Subproblem 1
Set the factor '(-17 + -2p)' equal to zero and attempt to solve:

Simplifying
-17 + -2p = 0

Solving
-17 + -2p = 0

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

Add '17' to each side of the equation.
-17 + 17 + -2p = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -2p = 0 + 17
-2p = 0 + 17

Combine like terms: 0 + 17 = 17
-2p = 17

Divide each side by '-2'.
p = -8.5

Simplifying
p = -8.5
Subproblem 2
Set the factor '(1 + -2p)' equal to zero and attempt to solve:

Simplifying
1 + -2p = 0

Solving
1 + -2p = 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 + -2p = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2p = 0 + -1
-2p = 0 + -1

Combine like terms: 0 + -1 = -1
-2p = -1

Divide each side by '-2'.
p = 0.5

Simplifying
p = 0.5
Solution
p = {-8.5, 0.5}