6p^2-31p+18=0

Solution for 6p^2-31p+18=0 equation:

Simplifying
6p2 + -31p + 18 = 0

Reorder the terms:
18 + -31p + 6p2 = 0

Solving
18 + -31p + 6p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(2 + -3p)(9 + -2p) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + -2p)' equal to zero and attempt to solve:

Simplifying
9 + -2p = 0

Solving
9 + -2p = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2p = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2p = 0 + -9
-2p = 0 + -9

Combine like terms: 0 + -9 = -9
-2p = -9

Divide each side by '-2'.
p = 4.5

Simplifying
p = 4.5
Solution
p = {0.6666666667, 4.5}