(x-2)(3x+1)-(x+1)(3x-1)=0

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Solution for (x-2)(3x+1)-(x+1)(3x-1)=0 equation: 


Simplifying
(x + -2)(3x + 1) + -1(x + 1)(3x + -1) = 0

Reorder the terms:
(-2 + x)(3x + 1) + -1(x + 1)(3x + -1) = 0

Reorder the terms:
(-2 + x)(1 + 3x) + -1(x + 1)(3x + -1) = 0

Multiply (-2 + x) * (1 + 3x)
(-2(1 + 3x) + x(1 + 3x)) + -1(x + 1)(3x + -1) = 0
((1 * -2 + 3x * -2) + x(1 + 3x)) + -1(x + 1)(3x + -1) = 0
((-2 + -6x) + x(1 + 3x)) + -1(x + 1)(3x + -1) = 0
(-2 + -6x + (1 * x + 3x * x)) + -1(x + 1)(3x + -1) = 0
(-2 + -6x + (1x + 3x2)) + -1(x + 1)(3x + -1) = 0

Combine like terms: -6x + 1x = -5x
(-2 + -5x + 3x2) + -1(x + 1)(3x + -1) = 0

Reorder the terms:
-2 + -5x + 3x2 + -1(1 + x)(3x + -1) = 0

Reorder the terms:
-2 + -5x + 3x2 + -1(1 + x)(-1 + 3x) = 0

Multiply (1 + x) * (-1 + 3x)
-2 + -5x + 3x2 + -1(1(-1 + 3x) + x(-1 + 3x)) = 0
-2 + -5x + 3x2 + -1((-1 * 1 + 3x * 1) + x(-1 + 3x)) = 0
-2 + -5x + 3x2 + -1((-1 + 3x) + x(-1 + 3x)) = 0
-2 + -5x + 3x2 + -1(-1 + 3x + (-1 * x + 3x * x)) = 0
-2 + -5x + 3x2 + -1(-1 + 3x + (-1x + 3x2)) = 0

Combine like terms: 3x + -1x = 2x
-2 + -5x + 3x2 + -1(-1 + 2x + 3x2) = 0
-2 + -5x + 3x2 + (-1 * -1 + 2x * -1 + 3x2 * -1) = 0
-2 + -5x + 3x2 + (1 + -2x + -3x2) = 0

Reorder the terms:
-2 + 1 + -5x + -2x + 3x2 + -3x2 = 0

Combine like terms: -2 + 1 = -1
-1 + -5x + -2x + 3x2 + -3x2 = 0

Combine like terms: -5x + -2x = -7x
-1 + -7x + 3x2 + -3x2 = 0

Combine like terms: 3x2 + -3x2 = 0
-1 + -7x + 0 = 0
-1 + -7x = 0

Solving
-1 + -7x = 0

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + -7x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7x = 0 + 1
-7x = 0 + 1

Combine like terms: 0 + 1 = 1
-7x = 1

Divide each side by '-7'.
x = -0.1428571429

Simplifying
x = -0.1428571429

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