6((p*p)-1)=5p

Solution for 6((p*p)-1)=5p equation:

Simplifying
6((p * p) + -1) = 5p

Multiply p * p
6((p2) + -1) = 5p
6(p2 + -1) = 5p

Reorder the terms:
6(-1 + p2) = 5p
(-1 * 6 + p2 * 6) = 5p
(-6 + 6p2) = 5p

Solving
-6 + 6p2 = 5p

Solving for variable 'p'.

Reorder the terms:
-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}