sqrt((7*x)+1)-sqrt(x-5)=6

Solution for sqrt((7*x)+1)-sqrt(x-5)=6 equation:

Simplifying
sqrt((7x) + 1) + -1sqrt(x + -5) = 6

Reorder the terms:
qrst(1 + (7x)) + -1sqrt(x + -5) = 6
(1 * qrst + (7x) * qrst) + -1sqrt(x + -5) = 6
(1qrst + 7qrstx) + -1sqrt(x + -5) = 6

Reorder the terms:
1qrst + 7qrstx + -1qrst(-5 + x) = 6
1qrst + 7qrstx + (-5 * -1qrst + x * -1qrst) = 6
1qrst + 7qrstx + (5qrst + -1qrstx) = 6

Reorder the terms:
1qrst + 5qrst + 7qrstx + -1qrstx = 6

Combine like terms: 1qrst + 5qrst = 6qrst
6qrst + 7qrstx + -1qrstx = 6

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

Solving
6qrst + 6qrstx = 6

Solving for variable 'q'.

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

Reorder the terms:
-6 + 6qrst + 6qrstx = 6 + -6

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

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

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + qrst + qrstx)' equal to zero and attempt to solve:

Simplifying
-1 + qrst + qrstx = 0

Solving
-1 + qrst + qrstx = 0

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

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

Reorder the terms:
-1 + 1 + qrst + qrstx = 0 + 1

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

Combine like terms: 0 + 1 = 1
qrst + qrstx = 1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.