10s^2-33sb+20b^2=0

Solution for 10s^2-33sb+20b^2=0 equation:

Simplifying
10s2 + -33sb + 20b2 = 0

Reorder the terms:
-33bs + 20b2 + 10s2 = 0

Solving
-33bs + 20b2 + 10s2 = 0

Solving for variable 'b'.

Factor a trinomial.
(4b + -5s)(5b + -2s) = 0

Subproblem 1
Set the factor '(4b + -5s)' equal to zero and attempt to solve:

Simplifying
4b + -5s = 0

Solving
4b + -5s = 0

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

Add '5s' to each side of the equation.
4b + -5s + 5s = 0 + 5s

Combine like terms: -5s + 5s = 0
4b + 0 = 0 + 5s
4b = 0 + 5s
Remove the zero:
4b = 5s

Divide each side by '4'.
b = 1.25s

Simplifying
b = 1.25s
Subproblem 2
Set the factor '(5b + -2s)' equal to zero and attempt to solve:

Simplifying
5b + -2s = 0

Solving
5b + -2s = 0

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

Add '2s' to each side of the equation.
5b + -2s + 2s = 0 + 2s

Combine like terms: -2s + 2s = 0
5b + 0 = 0 + 2s
5b = 0 + 2s
Remove the zero:
5b = 2s

Divide each side by '5'.
b = 0.4s

Simplifying
b = 0.4s
Solution
b = {1.25s, 0.4s}