sqrt(5x^2-5x+3)-sqrt(7x-2)+4x^2-6x+1=0

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Solution for sqrt(5x^2-5x+3)-sqrt(7x-2)+4x^2-6x+1=0 equation: 


Simplifying
sqrt(5x2 + -5x + 3) + -1sqrt(7x + -2) + 4x2 + -6x + 1 = 0

Reorder the terms:
qrst(3 + -5x + 5x2) + -1sqrt(7x + -2) + 4x2 + -6x + 1 = 0
(3 * qrst + -5x * qrst + 5x2 * qrst) + -1sqrt(7x + -2) + 4x2 + -6x + 1 = 0
(3qrst + -5qrstx + 5qrstx2) + -1sqrt(7x + -2) + 4x2 + -6x + 1 = 0

Reorder the terms:
3qrst + -5qrstx + 5qrstx2 + -1qrst(-2 + 7x) + 4x2 + -6x + 1 = 0
3qrst + -5qrstx + 5qrstx2 + (-2 * -1qrst + 7x * -1qrst) + 4x2 + -6x + 1 = 0
3qrst + -5qrstx + 5qrstx2 + (2qrst + -7qrstx) + 4x2 + -6x + 1 = 0

Reorder the terms:
1 + 3qrst + 2qrst + -5qrstx + -7qrstx + 5qrstx2 + -6x + 4x2 = 0

Combine like terms: 3qrst + 2qrst = 5qrst
1 + 5qrst + -5qrstx + -7qrstx + 5qrstx2 + -6x + 4x2 = 0

Combine like terms: -5qrstx + -7qrstx = -12qrstx
1 + 5qrst + -12qrstx + 5qrstx2 + -6x + 4x2 = 0

Solving
1 + 5qrst + -12qrstx + 5qrstx2 + -6x + 4x2 = 0

Solving for variable 'q'.

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

Add '-1' to each side of the equation.
1 + 5qrst + -12qrstx + 5qrstx2 + -6x + -1 + 4x2 = 0 + -1

Reorder the terms:
1 + -1 + 5qrst + -12qrstx + 5qrstx2 + -6x + 4x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5qrst + -12qrstx + 5qrstx2 + -6x + 4x2 = 0 + -1
5qrst + -12qrstx + 5qrstx2 + -6x + 4x2 = 0 + -1

Combine like terms: 0 + -1 = -1
5qrst + -12qrstx + 5qrstx2 + -6x + 4x2 = -1

Add '6x' to each side of the equation.
5qrst + -12qrstx + 5qrstx2 + -6x + 6x + 4x2 = -1 + 6x

Combine like terms: -6x + 6x = 0
5qrst + -12qrstx + 5qrstx2 + 0 + 4x2 = -1 + 6x
5qrst + -12qrstx + 5qrstx2 + 4x2 = -1 + 6x

Add '-4x2' to each side of the equation.
5qrst + -12qrstx + 5qrstx2 + 4x2 + -4x2 = -1 + 6x + -4x2

Combine like terms: 4x2 + -4x2 = 0
5qrst + -12qrstx + 5qrstx2 + 0 = -1 + 6x + -4x2
5qrst + -12qrstx + 5qrstx2 = -1 + 6x + -4x2

Reorder the terms:
1 + 5qrst + -12qrstx + 5qrstx2 + -6x + 4x2 = -1 + 6x + -4x2 + 1 + -6x + 4x2

Reorder the terms:
1 + 5qrst + -12qrstx + 5qrstx2 + -6x + 4x2 = -1 + 1 + 6x + -6x + -4x2 + 4x2

Combine like terms: -1 + 1 = 0
1 + 5qrst + -12qrstx + 5qrstx2 + -6x + 4x2 = 0 + 6x + -6x + -4x2 + 4x2
1 + 5qrst + -12qrstx + 5qrstx2 + -6x + 4x2 = 6x + -6x + -4x2 + 4x2

Combine like terms: 6x + -6x = 0
1 + 5qrst + -12qrstx + 5qrstx2 + -6x + 4x2 = 0 + -4x2 + 4x2
1 + 5qrst + -12qrstx + 5qrstx2 + -6x + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
1 + 5qrst + -12qrstx + 5qrstx2 + -6x + 4x2 = 0

The solution to this equation could not be determined.

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