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

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


Simplifying
2x2 + -3x + -1(3x + -1)(x + -2) = 0

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

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

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

Combine like terms: -1x + -6x = -7x
2x2 + -3x + -1(2 + -7x + 3x2) = 0
2x2 + -3x + (2 * -1 + -7x * -1 + 3x2 * -1) = 0
2x2 + -3x + (-2 + 7x + -3x2) = 0

Reorder the terms:
-2 + -3x + 7x + 2x2 + -3x2 = 0

Combine like terms: -3x + 7x = 4x
-2 + 4x + 2x2 + -3x2 = 0

Combine like terms: 2x2 + -3x2 = -1x2
-2 + 4x + -1x2 = 0

Solving
-2 + 4x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
2 + -4x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -4x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -4x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -4x + x2 = 0 + -2
-4x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-4x + x2 = -2

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -2 + 4

Reorder the terms:
4 + -4x + x2 = -2 + 4

Combine like terms: -2 + 4 = 2
4 + -4x + x2 = 2

Factor a perfect square on the left side:
(x + -2)(x + -2) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + -2) equal to 1.414213562 and -1.414213562.


Subproblem 1
x + -2 = 1.414213562

Simplifying
x + -2 = 1.414213562

Reorder the terms:
-2 + x = 1.414213562

Solving
-2 + x = 1.414213562

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 1.414213562 + 2

Combine like terms: -2 + 2 = 0
0 + x = 1.414213562 + 2
x = 1.414213562 + 2

Combine like terms: 1.414213562 + 2 = 3.414213562
x = 3.414213562

Simplifying
x = 3.414213562


Subproblem 2
x + -2 = -1.414213562

Simplifying
x + -2 = -1.414213562

Reorder the terms:
-2 + x = -1.414213562

Solving
-2 + x = -1.414213562

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -1.414213562 + 2

Combine like terms: -2 + 2 = 0
0 + x = -1.414213562 + 2
x = -1.414213562 + 2

Combine like terms: -1.414213562 + 2 = 0.585786438
x = 0.585786438

Simplifying
x = 0.585786438


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.414213562, 0.585786438}

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