sqrt(1-6x)-sqrt(x+8)=3

Solution for sqrt(1-6x)-sqrt(x+8)=3 equation:

Simplifying
sqrt(1 + -6x) + -1sqrt(x + 8) = 3
(1 * qrst + -6x * qrst) + -1sqrt(x + 8) = 3
(1qrst + -6qrstx) + -1sqrt(x + 8) = 3

Reorder the terms:
1qrst + -6qrstx + -1qrst(8 + x) = 3
1qrst + -6qrstx + (8 * -1qrst + x * -1qrst) = 3
1qrst + -6qrstx + (-8qrst + -1qrstx) = 3

Reorder the terms:
1qrst + -8qrst + -6qrstx + -1qrstx = 3

Combine like terms: 1qrst + -8qrst = -7qrst
-7qrst + -6qrstx + -1qrstx = 3

Combine like terms: -6qrstx + -1qrstx = -7qrstx
-7qrst + -7qrstx = 3

Solving
-7qrst + -7qrstx = 3

Solving for variable 'q'.

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

Reorder the terms:
-3 + -7qrst + -7qrstx = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -7qrst + -7qrstx = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 7qrst + 7qrstx) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 7qrst + 7qrstx)' equal to zero and attempt to solve:

Simplifying
3 + 7qrst + 7qrstx = 0

Solving
3 + 7qrst + 7qrstx = 0

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

Add '-3' to each side of the equation.
3 + 7qrst + -3 + 7qrstx = 0 + -3

Reorder the terms:
3 + -3 + 7qrst + 7qrstx = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7qrst + 7qrstx = 0 + -3
7qrst + 7qrstx = 0 + -3

Combine like terms: 0 + -3 = -3
7qrst + 7qrstx = -3

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.