3x(x-2)=5(x-3)

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


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

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

Reorder the terms:
-6x + 3x2 = 5(-3 + x)
-6x + 3x2 = (-3 * 5 + x * 5)
-6x + 3x2 = (-15 + 5x)

Solving
-6x + 3x2 = -15 + 5x

Solving for variable 'x'.

Reorder the terms:
15 + -6x + -5x + 3x2 = -15 + 5x + 15 + -5x

Combine like terms: -6x + -5x = -11x
15 + -11x + 3x2 = -15 + 5x + 15 + -5x

Reorder the terms:
15 + -11x + 3x2 = -15 + 15 + 5x + -5x

Combine like terms: -15 + 15 = 0
15 + -11x + 3x2 = 0 + 5x + -5x
15 + -11x + 3x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
15 + -11x + 3x2 = 0

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

Divide each side by '3'.
5 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -3.666666667x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -3.666666667x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3.666666667x + x2 = 0 + -5
-3.666666667x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-3.666666667x + x2 = -5

The x term is -3.666666667x.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667x + 3.361111114 + x2 = -5 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = -5 + 3.361111114

Combine like terms: -5 + 3.361111114 = -1.638888886
3.361111114 + -3.666666667x + x2 = -1.638888886

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = -1.638888886

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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