x(3x-5)=5x-28

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Solution for x(3x-5)=5x-28 equation: 


Simplifying
x(3x + -5) = 5x + -28

Reorder the terms:
x(-5 + 3x) = 5x + -28
(-5 * x + 3x * x) = 5x + -28
(-5x + 3x2) = 5x + -28

Reorder the terms:
-5x + 3x2 = -28 + 5x

Solving
-5x + 3x2 = -28 + 5x

Solving for variable 'x'.

Reorder the terms:
28 + -5x + -5x + 3x2 = -28 + 5x + 28 + -5x

Combine like terms: -5x + -5x = -10x
28 + -10x + 3x2 = -28 + 5x + 28 + -5x

Reorder the terms:
28 + -10x + 3x2 = -28 + 28 + 5x + -5x

Combine like terms: -28 + 28 = 0
28 + -10x + 3x2 = 0 + 5x + -5x
28 + -10x + 3x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
28 + -10x + 3x2 = 0

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

Divide each side by '3'.
9.333333333 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '-9.333333333' to each side of the equation.
9.333333333 + -3.333333333x + -9.333333333 + x2 = 0 + -9.333333333

Reorder the terms:
9.333333333 + -9.333333333 + -3.333333333x + x2 = 0 + -9.333333333

Combine like terms: 9.333333333 + -9.333333333 = 0.000000000
0.000000000 + -3.333333333x + x2 = 0 + -9.333333333
-3.333333333x + x2 = 0 + -9.333333333

Combine like terms: 0 + -9.333333333 = -9.333333333
-3.333333333x + x2 = -9.333333333

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = -9.333333333 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = -9.333333333 + 2.777777779

Combine like terms: -9.333333333 + 2.777777779 = -6.555555554
2.777777779 + -3.333333333x + x2 = -6.555555554

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = -6.555555554

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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