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

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

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

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

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

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

Combine like terms: 3x + 4x = 7x
(2 + 7x + 6x2) = x + 292

Reorder the terms:
2 + 7x + 6x2 = 292 + x

Solving
2 + 7x + 6x2 = 292 + x

Solving for variable 'x'.

Reorder the terms:
2 + -292 + 7x + -1x + 6x2 = 292 + x + -292 + -1x

Combine like terms: 2 + -292 = -290
-290 + 7x + -1x + 6x2 = 292 + x + -292 + -1x

Combine like terms: 7x + -1x = 6x
-290 + 6x + 6x2 = 292 + x + -292 + -1x

Reorder the terms:
-290 + 6x + 6x2 = 292 + -292 + x + -1x

Combine like terms: 292 + -292 = 0
-290 + 6x + 6x2 = 0 + x + -1x
-290 + 6x + 6x2 = x + -1x

Combine like terms: x + -1x = 0
-290 + 6x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-145 + 3x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-145 + 3x + 3x2)' equal to zero and attempt to solve:

Simplifying
-145 + 3x + 3x2 = 0

Solving
-145 + 3x + 3x2 = 0

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

Divide each side by '3'.
-48.33333333 + x + x2 = 0

Move the constant term to the right:

Add '48.33333333' to each side of the equation.
-48.33333333 + x + 48.33333333 + x2 = 0 + 48.33333333

Reorder the terms:
-48.33333333 + 48.33333333 + x + x2 = 0 + 48.33333333

Combine like terms: -48.33333333 + 48.33333333 = 0.00000000
0.00000000 + x + x2 = 0 + 48.33333333
x + x2 = 0 + 48.33333333

Combine like terms: 0 + 48.33333333 = 48.33333333
x + x2 = 48.33333333

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

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 48.33333333 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 48.33333333 + 0.25

Combine like terms: 48.33333333 + 0.25 = 48.58333333
1.25 + x2 = 48.58333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 48.58333333

Calculate the square root of the right side: 6.970174555

Break this problem into two subproblems by setting 
(x + 0.5) equal to 6.970174555 and -6.970174555.

Subproblem 1
x + 0.5 = 6.970174555

Simplifying
x + 0.5 = 6.970174555

Reorder the terms:
0.5 + x = 6.970174555

Solving
0.5 + x = 6.970174555

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 6.970174555 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 6.970174555 + -0.5
x = 6.970174555 + -0.5

Combine like terms: 6.970174555 + -0.5 = 6.470174555
x = 6.470174555

Simplifying
x = 6.470174555

Subproblem 2
x + 0.5 = -6.970174555

Simplifying
x + 0.5 = -6.970174555

Reorder the terms:
0.5 + x = -6.970174555

Solving
0.5 + x = -6.970174555

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -6.970174555 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -6.970174555 + -0.5
x = -6.970174555 + -0.5

Combine like terms: -6.970174555 + -0.5 = -7.470174555
x = -7.470174555

Simplifying
x = -7.470174555

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.470174555, -7.470174555}
Solution
x = {6.470174555, -7.470174555}