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

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

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

Combine like terms: 8 + 2 = 10
3(-6 + 2x)[(10 + x + -3x) + -1] = 2 + -1(3 + -2x)

Combine like terms: x + -3x = -2x
3(-6 + 2x)[(10 + -2x) + -1] = 2 + -1(3 + -2x)

Remove parenthesis around (10 + -2x)
3(-6 + 2x)[10 + -2x + -1] = 2 + -1(3 + -2x)

Reorder the terms:
3(-6 + 2x)[10 + -1 + -2x] = 2 + -1(3 + -2x)

Combine like terms: 10 + -1 = 9
3(-6 + 2x)[9 + -2x] = 2 + -1(3 + -2x)

Multiply (-6 + 2x) * [9 + -2x]
3(-6[9 + -2x] + 2x * [9 + -2x]) = 2 + -1(3 + -2x)
3([9 * -6 + -2x * -6] + 2x * [9 + -2x]) = 2 + -1(3 + -2x)
3([-54 + 12x] + 2x * [9 + -2x]) = 2 + -1(3 + -2x)
3(-54 + 12x + [9 * 2x + -2x * 2x]) = 2 + -1(3 + -2x)
3(-54 + 12x + [18x + -4x2]) = 2 + -1(3 + -2x)

Combine like terms: 12x + 18x = 30x
3(-54 + 30x + -4x2) = 2 + -1(3 + -2x)
(-54 * 3 + 30x * 3 + -4x2 * 3) = 2 + -1(3 + -2x)
(-162 + 90x + -12x2) = 2 + -1(3 + -2x)
-162 + 90x + -12x2 = 2 + (3 * -1 + -2x * -1)
-162 + 90x + -12x2 = 2 + (-3 + 2x)

Combine like terms: 2 + -3 = -1
-162 + 90x + -12x2 = -1 + 2x

Solving
-162 + 90x + -12x2 = -1 + 2x

Solving for variable 'x'.

Reorder the terms:
-162 + 1 + 90x + -2x + -12x2 = -1 + 2x + 1 + -2x

Combine like terms: -162 + 1 = -161
-161 + 90x + -2x + -12x2 = -1 + 2x + 1 + -2x

Combine like terms: 90x + -2x = 88x
-161 + 88x + -12x2 = -1 + 2x + 1 + -2x

Reorder the terms:
-161 + 88x + -12x2 = -1 + 1 + 2x + -2x

Combine like terms: -1 + 1 = 0
-161 + 88x + -12x2 = 0 + 2x + -2x
-161 + 88x + -12x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-161 + 88x + -12x2 = 0

Factor a trinomial.
(-23 + 6x)(7 + -2x) = 0


Subproblem 1
Set the factor '(-23 + 6x)' equal to zero and attempt to solve:

Simplifying
-23 + 6x = 0

Solving
-23 + 6x = 0

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

Add '23' to each side of the equation.
-23 + 23 + 6x = 0 + 23

Combine like terms: -23 + 23 = 0
0 + 6x = 0 + 23
6x = 0 + 23

Combine like terms: 0 + 23 = 23
6x = 23

Divide each side by '6'.
x = 3.833333333

Simplifying
x = 3.833333333

Subproblem 2
Set the factor '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {3.833333333, 3.5}

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