6(1)(x-1)=3(x+1)(x-1)+(x+1)(1)(2)

Solution for 6(1)(x-1)=3(x+1)(x-1)+(x+1)(1)(2) equation:

Simplifying
6(1)(x + -1) = 3(x + 1)(x + -1) + (x + 1)(1)(2)

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

Multiply 6 * 1
6(-1 + x) = 3(x + 1)(x + -1) + (x + 1)(1)(2)
(-1 * 6 + x * 6) = 3(x + 1)(x + -1) + (x + 1)(1)(2)
(-6 + 6x) = 3(x + 1)(x + -1) + (x + 1)(1)(2)

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

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

Multiply (1 + x) * (-1 + x)
-6 + 6x = 3(1(-1 + x) + x(-1 + x)) + (x + 1)(1)(2)
-6 + 6x = 3((-1 * 1 + x * 1) + x(-1 + x)) + (x + 1)(1)(2)
-6 + 6x = 3((-1 + 1x) + x(-1 + x)) + (x + 1)(1)(2)
-6 + 6x = 3(-1 + 1x + (-1 * x + x * x)) + (x + 1)(1)(2)
-6 + 6x = 3(-1 + 1x + (-1x + x2)) + (x + 1)(1)(2)

Combine like terms: 1x + -1x = 0
-6 + 6x = 3(-1 + 0 + x2) + (x + 1)(1)(2)
-6 + 6x = 3(-1 + x2) + (x + 1)(1)(2)
-6 + 6x = (-1 * 3 + x2 * 3) + (x + 1)(1)(2)
-6 + 6x = (-3 + 3x2) + (x + 1)(1)(2)

Reorder the terms:
-6 + 6x = -3 + 3x2 + (1 + x)(1)(2)

Reorder the terms for easier multiplication:
-6 + 6x = -3 + 3x2 + 1 * 2(1 + x)

Multiply 1 * 2
-6 + 6x = -3 + 3x2 + 2(1 + x)
-6 + 6x = -3 + 3x2 + (1 * 2 + x * 2)
-6 + 6x = -3 + 3x2 + (2 + 2x)

Reorder the terms:
-6 + 6x = -3 + 2 + 2x + 3x2

Combine like terms: -3 + 2 = -1
-6 + 6x = -1 + 2x + 3x2

Solving
-6 + 6x = -1 + 2x + 3x2

Solving for variable 'x'.

Reorder the terms:
-6 + 1 + 6x + -2x + -3x2 = -1 + 2x + 3x2 + 1 + -2x + -3x2

Combine like terms: -6 + 1 = -5
-5 + 6x + -2x + -3x2 = -1 + 2x + 3x2 + 1 + -2x + -3x2

Combine like terms: 6x + -2x = 4x
-5 + 4x + -3x2 = -1 + 2x + 3x2 + 1 + -2x + -3x2

Reorder the terms:
-5 + 4x + -3x2 = -1 + 1 + 2x + -2x + 3x2 + -3x2

Combine like terms: -1 + 1 = 0
-5 + 4x + -3x2 = 0 + 2x + -2x + 3x2 + -3x2
-5 + 4x + -3x2 = 2x + -2x + 3x2 + -3x2

Combine like terms: 2x + -2x = 0
-5 + 4x + -3x2 = 0 + 3x2 + -3x2
-5 + 4x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-5 + 4x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
1.666666667 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.333333333x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -1.333333333x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -1.333333333x + x2 = 0 + -1.666666667
-1.333333333x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-1.333333333x + x2 = -1.666666667

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = -1.666666667 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = -1.666666667 + 0.4444444442

Combine like terms: -1.666666667 + 0.4444444442 = -1.2222222228
0.4444444442 + -1.333333333x + x2 = -1.2222222228

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = -1.2222222228

Can't calculate square root of the right side.

The solution to this equation could not be determined.