12s^2-36sp+27p^2=

Solution for 12s^2-36sp+27p^2= equation:

Simplifying
12s2 + -36sp + 27p2 = 0

Reorder the terms:
-36ps + 27p2 + 12s2 = 0

Solving
-36ps + 27p2 + 12s2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12ps + 9p2 + 4s2) = 0

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

Ignore the factor 3.
Subproblem 1
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
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 = {0.6666666667s, 0.6666666667s}