27s^2+48st+21t^2=

Solution for 27s^2+48st+21t^2= equation:

Simplifying
27s2 + 48st + 21t2 = 0

Reorder the terms:
48st + 27s2 + 21t2 = 0

Solving
48st + 27s2 + 21t2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '3'.
3(16st + 9s2 + 7t2) = 0

Factor a trinomial.
3((9s + 7t)(s + t)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(9s + 7t)' equal to zero and attempt to solve:

Simplifying
9s + 7t = 0

Solving
9s + 7t = 0

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

Add '-7t' to each side of the equation.
9s + 7t + -7t = 0 + -7t

Combine like terms: 7t + -7t = 0
9s + 0 = 0 + -7t
9s = 0 + -7t
Remove the zero:
9s = -7t

Divide each side by '9'.
s = -0.7777777778t

Simplifying
s = -0.7777777778t
Subproblem 2
Set the factor '(s + t)' equal to zero and attempt to solve:

Simplifying
s + t = 0

Solving
s + t = 0

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

Add '-1t' to each side of the equation.
s + t + -1t = 0 + -1t

Combine like terms: t + -1t = 0
s + 0 = 0 + -1t
s = 0 + -1t
Remove the zero:
s = -1t

Simplifying
s = -1t
Solution
s = {-0.7777777778t, -1t}