18s^2-27sr+10r^2=

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Solution for 18s^2-27sr+10r^2= equation: 


Simplifying
18s2 + -27sr + 10r2 = 0

Reorder the terms:
-27rs + 10r2 + 18s2 = 0

Solving
-27rs + 10r2 + 18s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(2r + -3s)(5r + -6s) = 0


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

Simplifying
2r + -3s = 0

Solving
2r + -3s = 0

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

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

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

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

Simplifying
r = 1.5s

Subproblem 2
Set the factor '(5r + -6s)' equal to zero and attempt to solve:

Simplifying
5r + -6s = 0

Solving
5r + -6s = 0

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

Add '6s' to each side of the equation.
5r + -6s + 6s = 0 + 6s

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

Divide each side by '5'.
r = 1.2s

Simplifying
r = 1.2s
Solution
r = {1.5s, 1.2s}

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