3(2x-6)[(x-(3x-8)2)-1]=2-(3-2x)

Solution for 3(2x-6)[(x-(3x-8)2)-1]=2-(3-2x) equation:

Simplifying
3(2x + -6)[(x + -1(3x + -8) * 2) + -1] = 2 + -1(3 + -2x)

Reorder the terms:
3(-6 + 2x)[(x + -1(3x + -8) * 2) + -1] = 2 + -1(3 + -2x)

Reorder the terms:
3(-6 + 2x)[(x + -1(-8 + 3x) * 2) + -1] = 2 + -1(3 + -2x)

Reorder the terms for easier multiplication:
3(-6 + 2x)[(x + -1 * 2(-8 + 3x)) + -1] = 2 + -1(3 + -2x)

Multiply -1 * 2
3(-6 + 2x)[(x + -2(-8 + 3x)) + -1] = 2 + -1(3 + -2x)
3(-6 + 2x)[(x + (-8 * -2 + 3x * -2)) + -1] = 2 + -1(3 + -2x)
3(-6 + 2x)[(x + (16 + -6x)) + -1] = 2 + -1(3 + -2x)

Reorder the terms:
3(-6 + 2x)[(16 + x + -6x) + -1] = 2 + -1(3 + -2x)

Combine like terms: x + -6x = -5x
3(-6 + 2x)[(16 + -5x) + -1] = 2 + -1(3 + -2x)

Remove parenthesis around (16 + -5x)
3(-6 + 2x)[16 + -5x + -1] = 2 + -1(3 + -2x)

Reorder the terms:
3(-6 + 2x)[16 + -1 + -5x] = 2 + -1(3 + -2x)

Combine like terms: 16 + -1 = 15
3(-6 + 2x)[15 + -5x] = 2 + -1(3 + -2x)

Multiply (-6 + 2x) * [15 + -5x]
3(-6[15 + -5x] + 2x * [15 + -5x]) = 2 + -1(3 + -2x)
3([15 * -6 + -5x * -6] + 2x * [15 + -5x]) = 2 + -1(3 + -2x)
3([-90 + 30x] + 2x * [15 + -5x]) = 2 + -1(3 + -2x)
3(-90 + 30x + [15 * 2x + -5x * 2x]) = 2 + -1(3 + -2x)
3(-90 + 30x + [30x + -10x2]) = 2 + -1(3 + -2x)

Combine like terms: 30x + 30x = 60x
3(-90 + 60x + -10x2) = 2 + -1(3 + -2x)
(-90 * 3 + 60x * 3 + -10x2 * 3) = 2 + -1(3 + -2x)
(-270 + 180x + -30x2) = 2 + -1(3 + -2x)
-270 + 180x + -30x2 = 2 + (3 * -1 + -2x * -1)
-270 + 180x + -30x2 = 2 + (-3 + 2x)

Combine like terms: 2 + -3 = -1
-270 + 180x + -30x2 = -1 + 2x

Solving
-270 + 180x + -30x2 = -1 + 2x

Solving for variable 'x'.

Reorder the terms:
-270 + 1 + 180x + -2x + -30x2 = -1 + 2x + 1 + -2x

Combine like terms: -270 + 1 = -269
-269 + 180x + -2x + -30x2 = -1 + 2x + 1 + -2x

Combine like terms: 180x + -2x = 178x
-269 + 178x + -30x2 = -1 + 2x + 1 + -2x

Reorder the terms:
-269 + 178x + -30x2 = -1 + 1 + 2x + -2x

Combine like terms: -1 + 1 = 0
-269 + 178x + -30x2 = 0 + 2x + -2x
-269 + 178x + -30x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-269 + 178x + -30x2 = 0

Begin completing the square.  Divide all terms by
-30 the coefficient of the squared term: 

Divide each side by '-30'.
8.966666667 + -5.933333333x + x2 = 0.0

Move the constant term to the right:

Add '-8.966666667' to each side of the equation.
8.966666667 + -5.933333333x + -8.966666667 + x2 = 0.0 + -8.966666667

Reorder the terms:
8.966666667 + -8.966666667 + -5.933333333x + x2 = 0.0 + -8.966666667

Combine like terms: 8.966666667 + -8.966666667 = 0.000000000
0.000000000 + -5.933333333x + x2 = 0.0 + -8.966666667
-5.933333333x + x2 = 0.0 + -8.966666667

Combine like terms: 0.0 + -8.966666667 = -8.966666667
-5.933333333x + x2 = -8.966666667

The x term is -5.933333333x.  Take half its coefficient (-2.966666667).
Square it (8.801111113) and add it to both sides.

Add '8.801111113' to each side of the equation.
-5.933333333x + 8.801111113 + x2 = -8.966666667 + 8.801111113

Reorder the terms:
8.801111113 + -5.933333333x + x2 = -8.966666667 + 8.801111113

Combine like terms: -8.966666667 + 8.801111113 = -0.165555554
8.801111113 + -5.933333333x + x2 = -0.165555554

Factor a perfect square on the left side:
(x + -2.966666667)(x + -2.966666667) = -0.165555554

Can't calculate square root of the right side.

The solution to this equation could not be determined.