-3x(x-1)+8(x-3)=6+7-5x

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Solution for -3x(x-1)+8(x-3)=6+7-5x equation: 


Simplifying
-3x(x + -1) + 8(x + -3) = 6 + 7 + -5x

Reorder the terms:
-3x(-1 + x) + 8(x + -3) = 6 + 7 + -5x
(-1 * -3x + x * -3x) + 8(x + -3) = 6 + 7 + -5x
(3x + -3x2) + 8(x + -3) = 6 + 7 + -5x

Reorder the terms:
3x + -3x2 + 8(-3 + x) = 6 + 7 + -5x
3x + -3x2 + (-3 * 8 + x * 8) = 6 + 7 + -5x
3x + -3x2 + (-24 + 8x) = 6 + 7 + -5x

Reorder the terms:
-24 + 3x + 8x + -3x2 = 6 + 7 + -5x

Combine like terms: 3x + 8x = 11x
-24 + 11x + -3x2 = 6 + 7 + -5x

Combine like terms: 6 + 7 = 13
-24 + 11x + -3x2 = 13 + -5x

Solving
-24 + 11x + -3x2 = 13 + -5x

Solving for variable 'x'.

Reorder the terms:
-24 + -13 + 11x + 5x + -3x2 = 13 + -5x + -13 + 5x

Combine like terms: -24 + -13 = -37
-37 + 11x + 5x + -3x2 = 13 + -5x + -13 + 5x

Combine like terms: 11x + 5x = 16x
-37 + 16x + -3x2 = 13 + -5x + -13 + 5x

Reorder the terms:
-37 + 16x + -3x2 = 13 + -13 + -5x + 5x

Combine like terms: 13 + -13 = 0
-37 + 16x + -3x2 = 0 + -5x + 5x
-37 + 16x + -3x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-37 + 16x + -3x2 = 0

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

Divide each side by '-3'.
12.33333333 + -5.333333333x + x2 = 0

Move the constant term to the right:

Add '-12.33333333' to each side of the equation.
12.33333333 + -5.333333333x + -12.33333333 + x2 = 0 + -12.33333333

Reorder the terms:
12.33333333 + -12.33333333 + -5.333333333x + x2 = 0 + -12.33333333

Combine like terms: 12.33333333 + -12.33333333 = 0.00000000
0.00000000 + -5.333333333x + x2 = 0 + -12.33333333
-5.333333333x + x2 = 0 + -12.33333333

Combine like terms: 0 + -12.33333333 = -12.33333333
-5.333333333x + x2 = -12.33333333

The x term is -5.333333333x.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333x + 7.111111113 + x2 = -12.33333333 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333x + x2 = -12.33333333 + 7.111111113

Combine like terms: -12.33333333 + 7.111111113 = -5.222222217
7.111111113 + -5.333333333x + x2 = -5.222222217

Factor a perfect square on the left side:
(x + -2.666666667)(x + -2.666666667) = -5.222222217

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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