90s^2-195st+100t^2=

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Solution for 90s^2-195st+100t^2= equation: 


Simplifying
90s2 + -195st + 100t2 = 0

Reorder the terms:
-195st + 90s2 + 100t2 = 0

Solving
-195st + 90s2 + 100t2 = 0

Solving for variable 's'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-39st + 18s2 + 20t2) = 0

Factor a trinomial.
5((3s + -4t)(6s + -5t)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(3s + -4t)' equal to zero and attempt to solve:

Simplifying
3s + -4t = 0

Solving
3s + -4t = 0

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

Add '4t' to each side of the equation.
3s + -4t + 4t = 0 + 4t

Combine like terms: -4t + 4t = 0
3s + 0 = 0 + 4t
3s = 0 + 4t
Remove the zero:
3s = 4t

Divide each side by '3'.
s = 1.333333333t

Simplifying
s = 1.333333333t

Subproblem 2
Set the factor '(6s + -5t)' equal to zero and attempt to solve:

Simplifying
6s + -5t = 0

Solving
6s + -5t = 0

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

Add '5t' to each side of the equation.
6s + -5t + 5t = 0 + 5t

Combine like terms: -5t + 5t = 0
6s + 0 = 0 + 5t
6s = 0 + 5t
Remove the zero:
6s = 5t

Divide each side by '6'.
s = 0.8333333333t

Simplifying
s = 0.8333333333t
Solution
s = {1.333333333t, 0.8333333333t}

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