sqrt((sqrt(x))-1)=sqrt(x-7)

Solution for sqrt((sqrt(x))-1)=sqrt(x-7) equation:

Simplifying
sqrt((sqrt(x)) + -1) = sqrt(x + -7)

Multiply qrst * x
qrst((qrstx) + -1) = sqrt(x + -7)
qrst(qrstx + -1) = sqrt(x + -7)

Reorder the terms:
qrst(-1 + qrstx) = sqrt(x + -7)
(-1 * qrst + qrstx * qrst) = sqrt(x + -7)
(-1qrst + q2r2s2t2x) = sqrt(x + -7)

Reorder the terms:
-1qrst + q2r2s2t2x = qrst(-7 + x)
-1qrst + q2r2s2t2x = (-7 * qrst + x * qrst)
-1qrst + q2r2s2t2x = (-7qrst + qrstx)

Solving
-1qrst + q2r2s2t2x = -7qrst + qrstx

Solving for variable 'q'.

Reorder the terms:
-1qrst + 7qrst + -1qrstx + q2r2s2t2x = -7qrst + qrstx + 7qrst + -1qrstx

Combine like terms: -1qrst + 7qrst = 6qrst
6qrst + -1qrstx + q2r2s2t2x = -7qrst + qrstx + 7qrst + -1qrstx

Reorder the terms:
6qrst + -1qrstx + q2r2s2t2x = -7qrst + 7qrst + qrstx + -1qrstx

Combine like terms: -7qrst + 7qrst = 0
6qrst + -1qrstx + q2r2s2t2x = 0 + qrstx + -1qrstx
6qrst + -1qrstx + q2r2s2t2x = qrstx + -1qrstx

Combine like terms: qrstx + -1qrstx = 0
6qrst + -1qrstx + q2r2s2t2x = 0

Factor out the Greatest Common Factor (GCF), 'qrst'.
qrst(6 + -1x + qrstx) = 0

Subproblem 1
Set the factor 'qrst' equal to zero and attempt to solve:

Simplifying
qrst = 0

Solving
qrst = 0

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

Simplifying
qrst = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(6 + -1x + qrstx)' equal to zero and attempt to solve:

Simplifying
6 + -1x + qrstx = 0

Reorder the terms:
6 + qrstx + -1x = 0

Solving
6 + qrstx + -1x = 0

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

Add '-6' to each side of the equation.
6 + qrstx + -6 + -1x = 0 + -6

Reorder the terms:
6 + -6 + qrstx + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + qrstx + -1x = 0 + -6
qrstx + -1x = 0 + -6

Combine like terms: 0 + -6 = -6
qrstx + -1x = -6

Add 'x' to each side of the equation.
qrstx + -1x + x = -6 + x

Combine like terms: -1x + x = 0
qrstx + 0 = -6 + x
qrstx = -6 + x

Divide each side by 'rstx'.
q = -6r-1s-1t-1x-1 + r-1s-1t-1

Simplifying
q = -6r-1s-1t-1x-1 + r-1s-1t-1

Reorder the terms:
q = r-1s-1t-1 + -6r-1s-1t-1x-1
Solution
q = {r-1s-1t-1 + -6r-1s-1t-1x-1}