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

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


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

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

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

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

Combine like terms: -6x + 4x = -2x
(-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}

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