2(x-1)(3x+2)=x+292

Solution for 2(x-1)(3x+2)=x+292 equation:

Simplifying
2(x + -1)(3x + 2) = x + 292

Reorder the terms:
2(-1 + x)(3x + 2) = x + 292

Reorder the terms:
2(-1 + x)(2 + 3x) = x + 292

Multiply (-1 + x) * (2 + 3x)
2(-1(2 + 3x) + x(2 + 3x)) = x + 292
2((2 * -1 + 3x * -1) + x(2 + 3x)) = x + 292
2((-2 + -3x) + x(2 + 3x)) = x + 292
2(-2 + -3x + (2 * x + 3x * x)) = x + 292
2(-2 + -3x + (2x + 3x2)) = x + 292

Combine like terms: -3x + 2x = -1x
2(-2 + -1x + 3x2) = x + 292
(-2 * 2 + -1x * 2 + 3x2 * 2) = x + 292
(-4 + -2x + 6x2) = x + 292

Reorder the terms:
-4 + -2x + 6x2 = 292 + x

Solving
-4 + -2x + 6x2 = 292 + x

Solving for variable 'x'.

Reorder the terms:
-4 + -292 + -2x + -1x + 6x2 = 292 + x + -292 + -1x

Combine like terms: -4 + -292 = -296
-296 + -2x + -1x + 6x2 = 292 + x + -292 + -1x

Combine like terms: -2x + -1x = -3x
-296 + -3x + 6x2 = 292 + x + -292 + -1x

Reorder the terms:
-296 + -3x + 6x2 = 292 + -292 + x + -1x

Combine like terms: 292 + -292 = 0
-296 + -3x + 6x2 = 0 + x + -1x
-296 + -3x + 6x2 = x + -1x

Combine like terms: x + -1x = 0
-296 + -3x + 6x2 = 0

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

Divide each side by '6'.
-49.33333333 + -0.5x + x2 = 0

Move the constant term to the right:

Add '49.33333333' to each side of the equation.
-49.33333333 + -0.5x + 49.33333333 + x2 = 0 + 49.33333333

Reorder the terms:
-49.33333333 + 49.33333333 + -0.5x + x2 = 0 + 49.33333333

Combine like terms: -49.33333333 + 49.33333333 = 0.00000000
0.00000000 + -0.5x + x2 = 0 + 49.33333333
-0.5x + x2 = 0 + 49.33333333

Combine like terms: 0 + 49.33333333 = 49.33333333
-0.5x + x2 = 49.33333333

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 49.33333333 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 49.33333333 + 0.0625

Combine like terms: 49.33333333 + 0.0625 = 49.39583333
0.0625 + -0.5x + x2 = 49.39583333

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 49.39583333

Calculate the square root of the right side: 7.028216938

Break this problem into two subproblems by setting 
(x + -0.25) equal to 7.028216938 and -7.028216938.

Subproblem 1
x + -0.25 = 7.028216938

Simplifying
x + -0.25 = 7.028216938

Reorder the terms:
-0.25 + x = 7.028216938

Solving
-0.25 + x = 7.028216938

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 7.028216938 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 7.028216938 + 0.25
x = 7.028216938 + 0.25

Combine like terms: 7.028216938 + 0.25 = 7.278216938
x = 7.278216938

Simplifying
x = 7.278216938

Subproblem 2
x + -0.25 = -7.028216938

Simplifying
x + -0.25 = -7.028216938

Reorder the terms:
-0.25 + x = -7.028216938

Solving
-0.25 + x = -7.028216938

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -7.028216938 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -7.028216938 + 0.25
x = -7.028216938 + 0.25

Combine like terms: -7.028216938 + 0.25 = -6.778216938
x = -6.778216938

Simplifying
x = -6.778216938

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.278216938, -6.778216938}