2(2x-1)-3sqrt(5x-6)=sqrt(3x-8)

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Solution for 2(2x-1)-3sqrt(5x-6)=sqrt(3x-8) equation:


Simplifying
2(2x + -1) + -3sqrt(5x + -6) = sqrt(3x + -8)

Reorder the terms:
2(-1 + 2x) + -3sqrt(5x + -6) = sqrt(3x + -8)
(-1 * 2 + 2x * 2) + -3sqrt(5x + -6) = sqrt(3x + -8)
(-2 + 4x) + -3sqrt(5x + -6) = sqrt(3x + -8)

Reorder the terms:
-2 + 4x + -3qrst(-6 + 5x) = sqrt(3x + -8)
-2 + 4x + (-6 * -3qrst + 5x * -3qrst) = sqrt(3x + -8)
-2 + 4x + (18qrst + -15qrstx) = sqrt(3x + -8)

Reorder the terms:
-2 + 18qrst + -15qrstx + 4x = sqrt(3x + -8)

Reorder the terms:
-2 + 18qrst + -15qrstx + 4x = qrst(-8 + 3x)
-2 + 18qrst + -15qrstx + 4x = (-8 * qrst + 3x * qrst)
-2 + 18qrst + -15qrstx + 4x = (-8qrst + 3qrstx)

Solving
-2 + 18qrst + -15qrstx + 4x = -8qrst + 3qrstx

Solving for variable 'q'.

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

Add '8qrst' to each side of the equation.
-2 + 18qrst + -15qrstx + 8qrst + 4x = -8qrst + 8qrst + 3qrstx

Reorder the terms:
-2 + 18qrst + 8qrst + -15qrstx + 4x = -8qrst + 8qrst + 3qrstx

Combine like terms: 18qrst + 8qrst = 26qrst
-2 + 26qrst + -15qrstx + 4x = -8qrst + 8qrst + 3qrstx

Combine like terms: -8qrst + 8qrst = 0
-2 + 26qrst + -15qrstx + 4x = 0 + 3qrstx
-2 + 26qrst + -15qrstx + 4x = 3qrstx

Add '-3qrstx' to each side of the equation.
-2 + 26qrst + -15qrstx + -3qrstx + 4x = 3qrstx + -3qrstx

Combine like terms: -15qrstx + -3qrstx = -18qrstx
-2 + 26qrst + -18qrstx + 4x = 3qrstx + -3qrstx

Combine like terms: 3qrstx + -3qrstx = 0
-2 + 26qrst + -18qrstx + 4x = 0

Add '2' to each side of the equation.
-2 + 26qrst + -18qrstx + 2 + 4x = 0 + 2

Reorder the terms:
-2 + 2 + 26qrst + -18qrstx + 4x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 26qrst + -18qrstx + 4x = 0 + 2
26qrst + -18qrstx + 4x = 0 + 2

Combine like terms: 0 + 2 = 2
26qrst + -18qrstx + 4x = 2

Add '-4x' to each side of the equation.
26qrst + -18qrstx + 4x + -4x = 2 + -4x

Combine like terms: 4x + -4x = 0
26qrst + -18qrstx + 0 = 2 + -4x
26qrst + -18qrstx = 2 + -4x

Reorder the terms:
-2 + 26qrst + -18qrstx + 4x = 2 + -4x + -2 + 4x

Reorder the terms:
-2 + 26qrst + -18qrstx + 4x = 2 + -2 + -4x + 4x

Combine like terms: 2 + -2 = 0
-2 + 26qrst + -18qrstx + 4x = 0 + -4x + 4x
-2 + 26qrst + -18qrstx + 4x = -4x + 4x

Combine like terms: -4x + 4x = 0
-2 + 26qrst + -18qrstx + 4x = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 13qrst + -9qrstx + 2x) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + 13qrst + -9qrstx + 2x)' equal to zero and attempt to solve: Simplifying -1 + 13qrst + -9qrstx + 2x = 0 Solving -1 + 13qrst + -9qrstx + 2x = 0 Move all terms containing q to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 13qrst + -9qrstx + 1 + 2x = 0 + 1 Reorder the terms: -1 + 1 + 13qrst + -9qrstx + 2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 13qrst + -9qrstx + 2x = 0 + 1 13qrst + -9qrstx + 2x = 0 + 1 Combine like terms: 0 + 1 = 1 13qrst + -9qrstx + 2x = 1 Add '-2x' to each side of the equation. 13qrst + -9qrstx + 2x + -2x = 1 + -2x Combine like terms: 2x + -2x = 0 13qrst + -9qrstx + 0 = 1 + -2x 13qrst + -9qrstx = 1 + -2x 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.

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