(sqrt(x)-2)(sqrt(x)-3)=0

Solution for (sqrt(x)-2)(sqrt(x)-3)=0 equation:

Simplifying
(sqrt(x) + -2)(sqrt(x) + -3) = 0

Multiply qrst * x
(qrstx + -2)(sqrt(x) + -3) = 0

Reorder the terms:
(-2 + qrstx)(sqrt(x) + -3) = 0

Multiply qrst * x
(-2 + qrstx)(qrstx + -3) = 0

Reorder the terms:
(-2 + qrstx)(-3 + qrstx) = 0

Multiply (-2 + qrstx) * (-3 + qrstx)
(-2(-3 + qrstx) + qrstx(-3 + qrstx)) = 0
((-3 * -2 + qrstx * -2) + qrstx(-3 + qrstx)) = 0
((6 + -2qrstx) + qrstx(-3 + qrstx)) = 0
(6 + -2qrstx + (-3 * qrstx + qrstx * qrstx)) = 0
(6 + -2qrstx + (-3qrstx + q2r2s2t2x2)) = 0

Combine like terms: -2qrstx + -3qrstx = -5qrstx
(6 + -5qrstx + q2r2s2t2x2) = 0

Solving
6 + -5qrstx + q2r2s2t2x2 = 0

Solving for variable 'q'.

Factor a trinomial.
(2 + -1qrstx)(3 + -1qrstx) = 0

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

Simplifying
2 + -1qrstx = 0

Solving
2 + -1qrstx = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1qrstx = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1qrstx = 0 + -2
-1qrstx = 0 + -2

Combine like terms: 0 + -2 = -2
-1qrstx = -2

Divide each side by '-1rstx'.
q = 2r-1s-1t-1x-1

Simplifying
q = 2r-1s-1t-1x-1
Subproblem 2
Set the factor '(3 + -1qrstx)' equal to zero and attempt to solve:

Simplifying
3 + -1qrstx = 0

Solving
3 + -1qrstx = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1qrstx = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1qrstx = 0 + -3
-1qrstx = 0 + -3

Combine like terms: 0 + -3 = -3
-1qrstx = -3

Divide each side by '-1rstx'.
q = 3r-1s-1t-1x-1

Simplifying
q = 3r-1s-1t-1x-1
Solution
q = {2r-1s-1t-1x-1, 3r-1s-1t-1x-1}