5x-3x(2x-1)+3x=8+x

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Solution for 5x-3x(2x-1)+3x=8+x equation: 


Simplifying
5x + -3x(2x + -1) + 3x = 8 + x

Reorder the terms:
5x + -3x(-1 + 2x) + 3x = 8 + x
5x + (-1 * -3x + 2x * -3x) + 3x = 8 + x
5x + (3x + -6x2) + 3x = 8 + x

Reorder the terms:
5x + 3x + 3x + -6x2 = 8 + x

Combine like terms: 5x + 3x = 8x
8x + 3x + -6x2 = 8 + x

Combine like terms: 8x + 3x = 11x
11x + -6x2 = 8 + x

Solving
11x + -6x2 = 8 + x

Solving for variable 'x'.

Reorder the terms:
-8 + 11x + -1x + -6x2 = 8 + x + -8 + -1x

Combine like terms: 11x + -1x = 10x
-8 + 10x + -6x2 = 8 + x + -8 + -1x

Reorder the terms:
-8 + 10x + -6x2 = 8 + -8 + x + -1x

Combine like terms: 8 + -8 = 0
-8 + 10x + -6x2 = 0 + x + -1x
-8 + 10x + -6x2 = x + -1x

Combine like terms: x + -1x = 0
-8 + 10x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 5x + -3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + 5x + -3x2)' equal to zero and attempt to solve:

Simplifying
-4 + 5x + -3x2 = 0

Solving
-4 + 5x + -3x2 = 0

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

Divide each side by '-3'.
1.333333333 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + -1.666666667x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + -1.666666667x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + -1.666666667x + x2 = 0 + -1.333333333
-1.666666667x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
-1.666666667x + x2 = -1.333333333

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = -1.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = -1.333333333 + 0.6944444447

Combine like terms: -1.333333333 + 0.6944444447 = -0.6388888883
0.6944444447 + -1.666666667x + x2 = -0.6388888883

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = -0.6388888883

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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