19rs+r^2+90s^2=0

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Solution for 19rs+r^2+90s^2=0 equation: 


Simplifying
19rs + r2 + 90s2 = 0

Solving
19rs + r2 + 90s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(r + 9s)(r + 10s) = 0


Subproblem 1
Set the factor '(r + 9s)' equal to zero and attempt to solve:

Simplifying
r + 9s = 0

Solving
r + 9s = 0

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

Add '-9s' to each side of the equation.
r + 9s + -9s = 0 + -9s

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

Simplifying
r = -9s

Subproblem 2
Set the factor '(r + 10s)' equal to zero and attempt to solve:

Simplifying
r + 10s = 0

Solving
r + 10s = 0

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

Add '-10s' to each side of the equation.
r + 10s + -10s = 0 + -10s

Combine like terms: 10s + -10s = 0
r + 0 = 0 + -10s
r = 0 + -10s
Remove the zero:
r = -10s

Simplifying
r = -10s
Solution
r = {-9s, -10s}

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