8p^2-6=p(2p-5)

Solution for 8p^2-6=p(2p-5) equation:

Simplifying
8p2 + -6 = p(2p + -5)

Reorder the terms:
-6 + 8p2 = p(2p + -5)

Reorder the terms:
-6 + 8p2 = p(-5 + 2p)
-6 + 8p2 = (-5 * p + 2p * p)
-6 + 8p2 = (-5p + 2p2)

Solving
-6 + 8p2 = -5p + 2p2

Solving for variable 'p'.

Reorder the terms:
-6 + 5p + 8p2 + -2p2 = -5p + 2p2 + 5p + -2p2

Combine like terms: 8p2 + -2p2 = 6p2
-6 + 5p + 6p2 = -5p + 2p2 + 5p + -2p2

Reorder the terms:
-6 + 5p + 6p2 = -5p + 5p + 2p2 + -2p2

Combine like terms: -5p + 5p = 0
-6 + 5p + 6p2 = 0 + 2p2 + -2p2
-6 + 5p + 6p2 = 2p2 + -2p2

Combine like terms: 2p2 + -2p2 = 0
-6 + 5p + 6p2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
p = {-1.5, 0.6666666667}