(3X-1)(6X-1)=(6X+5)(3X+17)

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Solution for (3X-1)(6X-1)=(6X+5)(3X+17) equation: 


Simplifying
(3X + -1)(6X + -1) = (6X + 5)(3X + 17)

Reorder the terms:
(-1 + 3X)(6X + -1) = (6X + 5)(3X + 17)

Reorder the terms:
(-1 + 3X)(-1 + 6X) = (6X + 5)(3X + 17)

Multiply (-1 + 3X) * (-1 + 6X)
(-1(-1 + 6X) + 3X * (-1 + 6X)) = (6X + 5)(3X + 17)
((-1 * -1 + 6X * -1) + 3X * (-1 + 6X)) = (6X + 5)(3X + 17)
((1 + -6X) + 3X * (-1 + 6X)) = (6X + 5)(3X + 17)
(1 + -6X + (-1 * 3X + 6X * 3X)) = (6X + 5)(3X + 17)
(1 + -6X + (-3X + 18X2)) = (6X + 5)(3X + 17)

Combine like terms: -6X + -3X = -9X
(1 + -9X + 18X2) = (6X + 5)(3X + 17)

Reorder the terms:
1 + -9X + 18X2 = (5 + 6X)(3X + 17)

Reorder the terms:
1 + -9X + 18X2 = (5 + 6X)(17 + 3X)

Multiply (5 + 6X) * (17 + 3X)
1 + -9X + 18X2 = (5(17 + 3X) + 6X * (17 + 3X))
1 + -9X + 18X2 = ((17 * 5 + 3X * 5) + 6X * (17 + 3X))
1 + -9X + 18X2 = ((85 + 15X) + 6X * (17 + 3X))
1 + -9X + 18X2 = (85 + 15X + (17 * 6X + 3X * 6X))
1 + -9X + 18X2 = (85 + 15X + (102X + 18X2))

Combine like terms: 15X + 102X = 117X
1 + -9X + 18X2 = (85 + 117X + 18X2)

Add '-18X2' to each side of the equation.
1 + -9X + 18X2 + -18X2 = 85 + 117X + 18X2 + -18X2

Combine like terms: 18X2 + -18X2 = 0
1 + -9X + 0 = 85 + 117X + 18X2 + -18X2
1 + -9X = 85 + 117X + 18X2 + -18X2

Combine like terms: 18X2 + -18X2 = 0
1 + -9X = 85 + 117X + 0
1 + -9X = 85 + 117X

Solving
1 + -9X = 85 + 117X

Solving for variable 'X'.

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

Add '-117X' to each side of the equation.
1 + -9X + -117X = 85 + 117X + -117X

Combine like terms: -9X + -117X = -126X
1 + -126X = 85 + 117X + -117X

Combine like terms: 117X + -117X = 0
1 + -126X = 85 + 0
1 + -126X = 85

Add '-1' to each side of the equation.
1 + -1 + -126X = 85 + -1

Combine like terms: 1 + -1 = 0
0 + -126X = 85 + -1
-126X = 85 + -1

Combine like terms: 85 + -1 = 84
-126X = 84

Divide each side by '-126'.
X = -0.6666666667

Simplifying
X = -0.6666666667

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