6P^2=5P+6

Solution for 6P^2=5P+6 equation:

Simplifying
6P2 = 5P + 6

Reorder the terms:
6P2 = 6 + 5P

Solving
6P2 = 6 + 5P

Solving for variable 'P'.

Reorder the terms:
-6 + -5P + 6P2 = 6 + 5P + -6 + -5P

Reorder the terms:
-6 + -5P + 6P2 = 6 + -6 + 5P + -5P

Combine like terms: 6 + -6 = 0
-6 + -5P + 6P2 = 0 + 5P + -5P
-6 + -5P + 6P2 = 5P + -5P

Combine like terms: 5P + -5P = 0
-6 + -5P + 6P2 = 0

Factor a trinomial.
(-2 + -3P)(3 + -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 '(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 = {-0.6666666667, 1.5}