(6y-5p)(y)=(3p)(2p)

Solution for (6y-5p)(y)=(3p)(2p) equation:

Simplifying
(6y + -5p)(y) = (3p)(2p)

Reorder the terms:
(-5p + 6y)(y) = (3p)(2p)

Reorder the terms for easier multiplication:
y(-5p + 6y) = (3p)(2p)
(-5p * y + 6y * y) = (3p)(2p)
(-5py + 6y2) = (3p)(2p)

Remove parenthesis around (3p)
-5py + 6y2 = 3p(2p)

Remove parenthesis around (2p)
-5py + 6y2 = 3p * 2p

Reorder the terms for easier multiplication:
-5py + 6y2 = 3 * 2p * p

Multiply 3 * 2
-5py + 6y2 = 6p * p

Multiply p * p
-5py + 6y2 = 6p2

Solving
-5py + 6y2 = 6p2

Solving for variable 'p'.

Reorder the terms:
-5py + -6p2 + 6y2 = 6p2 + -6p2

Combine like terms: 6p2 + -6p2 = 0
-5py + -6p2 + 6y2 = 0

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

Subproblem 1
Set the factor '(-2p + -3y)' equal to zero and attempt to solve:

Simplifying
-2p + -3y = 0

Solving
-2p + -3y = 0

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

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

Combine like terms: -3y + 3y = 0
-2p + 0 = 0 + 3y
-2p = 0 + 3y
Remove the zero:
-2p = 3y

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

Simplifying
p = -1.5y
Subproblem 2
Set the factor '(3p + -2y)' equal to zero and attempt to solve:

Simplifying
3p + -2y = 0

Solving
3p + -2y = 0

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

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

Combine like terms: -2y + 2y = 0
3p + 0 = 0 + 2y
3p = 0 + 2y
Remove the zero:
3p = 2y

Divide each side by '3'.
p = 0.6666666667y

Simplifying
p = 0.6666666667y
Solution
p = {-1.5y, 0.6666666667y}