2x+4=8sqrt(3x+3)-6sqrt(5x+6)

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Solution for 2x+4=8sqrt(3x+3)-6sqrt(5x+6) equation:


Simplifying
2x + 4 = 8sqrt(3x + 3) + -6sqrt(5x + 6)

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

Reorder the terms:
4 + 2x = 8qrst(3 + 3x) + -6sqrt(5x + 6)
4 + 2x = (3 * 8qrst + 3x * 8qrst) + -6sqrt(5x + 6)
4 + 2x = (24qrst + 24qrstx) + -6sqrt(5x + 6)

Reorder the terms:
4 + 2x = 24qrst + 24qrstx + -6qrst(6 + 5x)
4 + 2x = 24qrst + 24qrstx + (6 * -6qrst + 5x * -6qrst)
4 + 2x = 24qrst + 24qrstx + (-36qrst + -30qrstx)

Reorder the terms:
4 + 2x = 24qrst + -36qrst + 24qrstx + -30qrstx

Combine like terms: 24qrst + -36qrst = -12qrst
4 + 2x = -12qrst + 24qrstx + -30qrstx

Combine like terms: 24qrstx + -30qrstx = -6qrstx
4 + 2x = -12qrst + -6qrstx

Solving
4 + 2x = -12qrst + -6qrstx

Solving for variable 'x'.

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

Add '6qrstx' to each side of the equation.
4 + 6qrstx + 2x = -12qrst + -6qrstx + 6qrstx

Combine like terms: -6qrstx + 6qrstx = 0
4 + 6qrstx + 2x = -12qrst + 0
4 + 6qrstx + 2x = -12qrst

Add '-4' to each side of the equation.
4 + 6qrstx + -4 + 2x = -4 + -12qrst

Reorder the terms:
4 + -4 + 6qrstx + 2x = -4 + -12qrst

Combine like terms: 4 + -4 = 0
0 + 6qrstx + 2x = -4 + -12qrst
6qrstx + 2x = -4 + -12qrst

Reorder the terms:
4 + 12qrst + 6qrstx + 2x = -4 + -12qrst + 4 + 12qrst

Reorder the terms:
4 + 12qrst + 6qrstx + 2x = -4 + 4 + -12qrst + 12qrst

Combine like terms: -4 + 4 = 0
4 + 12qrst + 6qrstx + 2x = 0 + -12qrst + 12qrst
4 + 12qrst + 6qrstx + 2x = -12qrst + 12qrst

Combine like terms: -12qrst + 12qrst = 0
4 + 12qrst + 6qrstx + 2x = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 6qrst + 3qrstx + x) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(2 + 6qrst + 3qrstx + x)' equal to zero and attempt to solve: Simplifying 2 + 6qrst + 3qrstx + x = 0 Solving 2 + 6qrst + 3qrstx + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + 6qrst + 3qrstx + -2 + x = 0 + -2 Reorder the terms: 2 + -2 + 6qrst + 3qrstx + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 6qrst + 3qrstx + x = 0 + -2 6qrst + 3qrstx + x = 0 + -2 Combine like terms: 0 + -2 = -2 6qrst + 3qrstx + x = -2 Add '-6qrst' to each side of the equation. 6qrst + 3qrstx + -6qrst + x = -2 + -6qrst Reorder the terms: 6qrst + -6qrst + 3qrstx + x = -2 + -6qrst Combine like terms: 6qrst + -6qrst = 0 0 + 3qrstx + x = -2 + -6qrst 3qrstx + x = -2 + -6qrst 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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