(4x^2-2x+8)-(x^2+3x-2)=x

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Solution for (4x^2-2x+8)-(x^2+3x-2)=x equation: 


Simplifying
(4x2 + -2x + 8) + -1(x2 + 3x + -2) = x

Reorder the terms:
(8 + -2x + 4x2) + -1(x2 + 3x + -2) = x

Remove parenthesis around (8 + -2x + 4x2)
8 + -2x + 4x2 + -1(x2 + 3x + -2) = x

Reorder the terms:
8 + -2x + 4x2 + -1(-2 + 3x + x2) = x
8 + -2x + 4x2 + (-2 * -1 + 3x * -1 + x2 * -1) = x
8 + -2x + 4x2 + (2 + -3x + -1x2) = x

Reorder the terms:
8 + 2 + -2x + -3x + 4x2 + -1x2 = x

Combine like terms: 8 + 2 = 10
10 + -2x + -3x + 4x2 + -1x2 = x

Combine like terms: -2x + -3x = -5x
10 + -5x + 4x2 + -1x2 = x

Combine like terms: 4x2 + -1x2 = 3x2
10 + -5x + 3x2 = x

Solving
10 + -5x + 3x2 = x

Solving for variable 'x'.

Reorder the terms:
10 + -5x + -1x + 3x2 = x + -1x

Combine like terms: -5x + -1x = -6x
10 + -6x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
10 + -6x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
3.333333333 + -2x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -2x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -2x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -2x + x2 = 0 + -3.333333333
-2x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-2x + x2 = -3.333333333

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -3.333333333 + 1

Reorder the terms:
1 + -2x + x2 = -3.333333333 + 1

Combine like terms: -3.333333333 + 1 = -2.333333333
1 + -2x + x2 = -2.333333333

Factor a perfect square on the left side:
(x + -1)(x + -1) = -2.333333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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