15x-10=6x(x+2)+(-x+3)

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Solution for 15x-10=6x(x+2)+(-x+3) equation: 


Simplifying
15x + -10 = 6x(x + 2) + (-1x + 3)

Reorder the terms:
-10 + 15x = 6x(x + 2) + (-1x + 3)

Reorder the terms:
-10 + 15x = 6x(2 + x) + (-1x + 3)
-10 + 15x = (2 * 6x + x * 6x) + (-1x + 3)
-10 + 15x = (12x + 6x2) + (-1x + 3)

Reorder the terms:
-10 + 15x = 12x + 6x2 + (3 + -1x)

Remove parenthesis around (3 + -1x)
-10 + 15x = 12x + 6x2 + 3 + -1x

Reorder the terms:
-10 + 15x = 3 + 12x + -1x + 6x2

Combine like terms: 12x + -1x = 11x
-10 + 15x = 3 + 11x + 6x2

Solving
-10 + 15x = 3 + 11x + 6x2

Solving for variable 'x'.

Reorder the terms:
-10 + -3 + 15x + -11x + -6x2 = 3 + 11x + 6x2 + -3 + -11x + -6x2

Combine like terms: -10 + -3 = -13
-13 + 15x + -11x + -6x2 = 3 + 11x + 6x2 + -3 + -11x + -6x2

Combine like terms: 15x + -11x = 4x
-13 + 4x + -6x2 = 3 + 11x + 6x2 + -3 + -11x + -6x2

Reorder the terms:
-13 + 4x + -6x2 = 3 + -3 + 11x + -11x + 6x2 + -6x2

Combine like terms: 3 + -3 = 0
-13 + 4x + -6x2 = 0 + 11x + -11x + 6x2 + -6x2
-13 + 4x + -6x2 = 11x + -11x + 6x2 + -6x2

Combine like terms: 11x + -11x = 0
-13 + 4x + -6x2 = 0 + 6x2 + -6x2
-13 + 4x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-13 + 4x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
2.166666667 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '-2.166666667' to each side of the equation.
2.166666667 + -0.6666666667x + -2.166666667 + x2 = 0 + -2.166666667

Reorder the terms:
2.166666667 + -2.166666667 + -0.6666666667x + x2 = 0 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + -0.6666666667x + x2 = 0 + -2.166666667
-0.6666666667x + x2 = 0 + -2.166666667

Combine like terms: 0 + -2.166666667 = -2.166666667
-0.6666666667x + x2 = -2.166666667

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = -2.166666667 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = -2.166666667 + 0.1111111112

Combine like terms: -2.166666667 + 0.1111111112 = -2.0555555558
0.1111111112 + -0.6666666667x + x2 = -2.0555555558

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = -2.0555555558

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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