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

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


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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

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

Factor a trinomial.
(-1 + -2x)(2 + -1x) = 0


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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.5, 2}

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