6p^2-13ps+6s^2=0

Solution for 6p^2-13ps+6s^2=0 equation:

Simplifying
6p2 + -13ps + 6s2 = 0

Reorder the terms:
-13ps + 6p2 + 6s2 = 0

Solving
-13ps + 6p2 + 6s2 = 0

Solving for variable 'p'.

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

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

Simplifying
2p + -3s = 0

Solving
2p + -3s = 0

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

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

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

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

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

Simplifying
3p + -2s = 0

Solving
3p + -2s = 0

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

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

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

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

Simplifying
p = 0.6666666667s
Solution
p = {1.5s, 0.6666666667s}