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

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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 = 1x
(-2 + 1x + 6x2) = x + 292

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

Solving
-2 + 1x + 6x2 = 292 + x

Solving for variable 'x'.

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

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

Combine like terms: 1x + -1x = 0
-294 + 0 + 6x2 = 292 + x + -292 + -1x
-294 + 6x2 = 292 + x + -292 + -1x

Reorder the terms:
-294 + 6x2 = 292 + -292 + x + -1x

Combine like terms: 292 + -292 = 0
-294 + 6x2 = 0 + x + -1x
-294 + 6x2 = x + -1x

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

Factor out the Greatest Common Factor (GCF), '6'.
6(-49 + x2) = 0

Factor a difference between two squares.
6((7 + x)(-7 + x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7
Solution
x = {-7, 7}

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