90q^2-195qr+100r^2=0

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Solution for 90q^2-195qr+100r^2=0 equation:


Simplifying
90q2 + -195qr + 100r2 = 0

Reorder the terms:
-195qr + 90q2 + 100r2 = 0

Solving
-195qr + 90q2 + 100r2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-39qr + 18q2 + 20r2) = 0

Factor a trinomial.
5((3q + -4r)(6q + -5r)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(3q + -4r)' equal to zero and attempt to solve: Simplifying 3q + -4r = 0 Solving 3q + -4r = 0 Move all terms containing q to the left, all other terms to the right. Add '4r' to each side of the equation. 3q + -4r + 4r = 0 + 4r Combine like terms: -4r + 4r = 0 3q + 0 = 0 + 4r 3q = 0 + 4r Remove the zero: 3q = 4r Divide each side by '3'. q = 1.333333333r Simplifying q = 1.333333333r

Subproblem 2

Set the factor '(6q + -5r)' equal to zero and attempt to solve: Simplifying 6q + -5r = 0 Solving 6q + -5r = 0 Move all terms containing q to the left, all other terms to the right. Add '5r' to each side of the equation. 6q + -5r + 5r = 0 + 5r Combine like terms: -5r + 5r = 0 6q + 0 = 0 + 5r 6q = 0 + 5r Remove the zero: 6q = 5r Divide each side by '6'. q = 0.8333333333r Simplifying q = 0.8333333333r

Solution

q = {1.333333333r, 0.8333333333r}

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