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

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

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

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

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

Multiply (-1 + 2x) * (2 + 3x)
(-1(2 + 3x) + 2x * (2 + 3x)) = 2 + 292
((2 * -1 + 3x * -1) + 2x * (2 + 3x)) = 2 + 292
((-2 + -3x) + 2x * (2 + 3x)) = 2 + 292
(-2 + -3x + (2 * 2x + 3x * 2x)) = 2 + 292
(-2 + -3x + (4x + 6x2)) = 2 + 292

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

Combine like terms: 2 + 292 = 294
-2 + 1x + 6x2 = 294

Solving
-2 + 1x + 6x2 = 294

Solving for variable 'x'.

Reorder the terms:
-2 + -294 + 1x + 6x2 = 294 + -294

Combine like terms: -2 + -294 = -296
-296 + 1x + 6x2 = 294 + -294

Combine like terms: 294 + -294 = 0
-296 + 1x + 6x2 = 0

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

Divide each side by '6'.
-49.33333333 + 0.1666666667x + x2 = 0

Move the constant term to the right:

Add '49.33333333' to each side of the equation.
-49.33333333 + 0.1666666667x + 49.33333333 + x2 = 0 + 49.33333333

Reorder the terms:
-49.33333333 + 49.33333333 + 0.1666666667x + x2 = 0 + 49.33333333

Combine like terms: -49.33333333 + 49.33333333 = 0.00000000
0.00000000 + 0.1666666667x + x2 = 0 + 49.33333333
0.1666666667x + x2 = 0 + 49.33333333

Combine like terms: 0 + 49.33333333 = 49.33333333
0.1666666667x + x2 = 49.33333333

The x term is 0.1666666667x.  Take half its coefficient (0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
0.1666666667x + 0.006944444447 + x2 = 49.33333333 + 0.006944444447

Reorder the terms:
0.006944444447 + 0.1666666667x + x2 = 49.33333333 + 0.006944444447

Combine like terms: 49.33333333 + 0.006944444447 = 49.340277774447
0.006944444447 + 0.1666666667x + x2 = 49.340277774447

Factor a perfect square on the left side:
(x + 0.08333333335)(x + 0.08333333335) = 49.340277774447

Calculate the square root of the right side: 7.024263504

Break this problem into two subproblems by setting 
(x + 0.08333333335) equal to 7.024263504 and -7.024263504.

Subproblem 1
x + 0.08333333335 = 7.024263504

Simplifying
x + 0.08333333335 = 7.024263504

Reorder the terms:
0.08333333335 + x = 7.024263504

Solving
0.08333333335 + x = 7.024263504

Solving for variable 'x'.

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

Add '-0.08333333335' to each side of the equation.
0.08333333335 + -0.08333333335 + x = 7.024263504 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = 7.024263504 + -0.08333333335
x = 7.024263504 + -0.08333333335

Combine like terms: 7.024263504 + -0.08333333335 = 6.94093017065
x = 6.94093017065

Simplifying
x = 6.94093017065

Subproblem 2
x + 0.08333333335 = -7.024263504

Simplifying
x + 0.08333333335 = -7.024263504

Reorder the terms:
0.08333333335 + x = -7.024263504

Solving
0.08333333335 + x = -7.024263504

Solving for variable 'x'.

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

Add '-0.08333333335' to each side of the equation.
0.08333333335 + -0.08333333335 + x = -7.024263504 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = -7.024263504 + -0.08333333335
x = -7.024263504 + -0.08333333335

Combine like terms: -7.024263504 + -0.08333333335 = -7.10759683735
x = -7.10759683735

Simplifying
x = -7.10759683735

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.94093017065, -7.10759683735}