51p=2p^2+72

Solution for 51p=2p^2+72 equation:

Simplifying
51p = 2p2 + 72

Reorder the terms:
51p = 72 + 2p2

Solving
51p = 72 + 2p2

Solving for variable 'p'.

Reorder the terms:
-72 + 51p + -2p2 = 72 + 2p2 + -72 + -2p2

Reorder the terms:
-72 + 51p + -2p2 = 72 + -72 + 2p2 + -2p2

Combine like terms: 72 + -72 = 0
-72 + 51p + -2p2 = 0 + 2p2 + -2p2
-72 + 51p + -2p2 = 2p2 + -2p2

Combine like terms: 2p2 + -2p2 = 0
-72 + 51p + -2p2 = 0

Factor a trinomial.
(-24 + p)(3 + -2p) = 0

Subproblem 1
Set the factor '(-24 + p)' equal to zero and attempt to solve:

Simplifying
-24 + p = 0

Solving
-24 + p = 0

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

Add '24' to each side of the equation.
-24 + 24 + p = 0 + 24

Combine like terms: -24 + 24 = 0
0 + p = 0 + 24
p = 0 + 24

Combine like terms: 0 + 24 = 24
p = 24

Simplifying
p = 24
Subproblem 2
Set the factor '(3 + -2p)' equal to zero and attempt to solve:

Simplifying
3 + -2p = 0

Solving
3 + -2p = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2p = 0 + -3

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

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

Divide each side by '-2'.
p = 1.5

Simplifying
p = 1.5
Solution
p = {24, 1.5}