3x(x-2)-x=2(x^2+1)+6

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Solution for 3x(x-2)-x=2(x^2+1)+6 equation: 


Simplifying
3x(x + -2) + -1x = 2(x2 + 1) + 6

Reorder the terms:
3x(-2 + x) + -1x = 2(x2 + 1) + 6
(-2 * 3x + x * 3x) + -1x = 2(x2 + 1) + 6
(-6x + 3x2) + -1x = 2(x2 + 1) + 6

Reorder the terms:
-6x + -1x + 3x2 = 2(x2 + 1) + 6

Combine like terms: -6x + -1x = -7x
-7x + 3x2 = 2(x2 + 1) + 6

Reorder the terms:
-7x + 3x2 = 2(1 + x2) + 6
-7x + 3x2 = (1 * 2 + x2 * 2) + 6
-7x + 3x2 = (2 + 2x2) + 6

Reorder the terms:
-7x + 3x2 = 2 + 6 + 2x2

Combine like terms: 2 + 6 = 8
-7x + 3x2 = 8 + 2x2

Solving
-7x + 3x2 = 8 + 2x2

Solving for variable 'x'.

Reorder the terms:
-8 + -7x + 3x2 + -2x2 = 8 + 2x2 + -8 + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-8 + -7x + 1x2 = 8 + 2x2 + -8 + -2x2

Reorder the terms:
-8 + -7x + 1x2 = 8 + -8 + 2x2 + -2x2

Combine like terms: 8 + -8 = 0
-8 + -7x + 1x2 = 0 + 2x2 + -2x2
-8 + -7x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-8 + -7x + 1x2 = 0

Factor a trinomial.
(-1 + -1x)(8 + -1x) = 0


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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = -1

Simplifying
x = -1

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-1, 8}

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