5p^2=31p-6

Solution for 5p^2=31p-6 equation:

Simplifying
5p2 = 31p + -6

Reorder the terms:
5p2 = -6 + 31p

Solving
5p2 = -6 + 31p

Solving for variable 'p'.

Reorder the terms:
6 + -31p + 5p2 = -6 + 31p + 6 + -31p

Reorder the terms:
6 + -31p + 5p2 = -6 + 6 + 31p + -31p

Combine like terms: -6 + 6 = 0
6 + -31p + 5p2 = 0 + 31p + -31p
6 + -31p + 5p2 = 31p + -31p

Combine like terms: 31p + -31p = 0
6 + -31p + 5p2 = 0

Factor a trinomial.
(1 + -5p)(6 + -1p) = 0

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

Simplifying
1 + -5p = 0

Solving
1 + -5p = 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 + -5p = 0 + -1

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

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

Divide each side by '-5'.
p = 0.2

Simplifying
p = 0.2
Subproblem 2
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
Solution
p = {0.2, 6}