(x+2)(2x+6)-(x-3)(x-6)=(x-3)(-10x+16)

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Solution for (x+2)(2x+6)-(x-3)(x-6)=(x-3)(-10x+16) equation: 


Simplifying
(x + 2)(2x + 6) + -1(x + -3)(x + -6) = (x + -3)(-10x + 16)

Reorder the terms:
(2 + x)(2x + 6) + -1(x + -3)(x + -6) = (x + -3)(-10x + 16)

Reorder the terms:
(2 + x)(6 + 2x) + -1(x + -3)(x + -6) = (x + -3)(-10x + 16)

Multiply (2 + x) * (6 + 2x)
(2(6 + 2x) + x(6 + 2x)) + -1(x + -3)(x + -6) = (x + -3)(-10x + 16)
((6 * 2 + 2x * 2) + x(6 + 2x)) + -1(x + -3)(x + -6) = (x + -3)(-10x + 16)
((12 + 4x) + x(6 + 2x)) + -1(x + -3)(x + -6) = (x + -3)(-10x + 16)
(12 + 4x + (6 * x + 2x * x)) + -1(x + -3)(x + -6) = (x + -3)(-10x + 16)
(12 + 4x + (6x + 2x2)) + -1(x + -3)(x + -6) = (x + -3)(-10x + 16)

Combine like terms: 4x + 6x = 10x
(12 + 10x + 2x2) + -1(x + -3)(x + -6) = (x + -3)(-10x + 16)

Reorder the terms:
12 + 10x + 2x2 + -1(-3 + x)(x + -6) = (x + -3)(-10x + 16)

Reorder the terms:
12 + 10x + 2x2 + -1(-3 + x)(-6 + x) = (x + -3)(-10x + 16)

Multiply (-3 + x) * (-6 + x)
12 + 10x + 2x2 + -1(-3(-6 + x) + x(-6 + x)) = (x + -3)(-10x + 16)
12 + 10x + 2x2 + -1((-6 * -3 + x * -3) + x(-6 + x)) = (x + -3)(-10x + 16)
12 + 10x + 2x2 + -1((18 + -3x) + x(-6 + x)) = (x + -3)(-10x + 16)
12 + 10x + 2x2 + -1(18 + -3x + (-6 * x + x * x)) = (x + -3)(-10x + 16)
12 + 10x + 2x2 + -1(18 + -3x + (-6x + x2)) = (x + -3)(-10x + 16)

Combine like terms: -3x + -6x = -9x
12 + 10x + 2x2 + -1(18 + -9x + x2) = (x + -3)(-10x + 16)
12 + 10x + 2x2 + (18 * -1 + -9x * -1 + x2 * -1) = (x + -3)(-10x + 16)
12 + 10x + 2x2 + (-18 + 9x + -1x2) = (x + -3)(-10x + 16)

Reorder the terms:
12 + -18 + 10x + 9x + 2x2 + -1x2 = (x + -3)(-10x + 16)

Combine like terms: 12 + -18 = -6
-6 + 10x + 9x + 2x2 + -1x2 = (x + -3)(-10x + 16)

Combine like terms: 10x + 9x = 19x
-6 + 19x + 2x2 + -1x2 = (x + -3)(-10x + 16)

Combine like terms: 2x2 + -1x2 = 1x2
-6 + 19x + 1x2 = (x + -3)(-10x + 16)

Reorder the terms:
-6 + 19x + 1x2 = (-3 + x)(-10x + 16)

Reorder the terms:
-6 + 19x + 1x2 = (-3 + x)(16 + -10x)

Multiply (-3 + x) * (16 + -10x)
-6 + 19x + 1x2 = (-3(16 + -10x) + x(16 + -10x))
-6 + 19x + 1x2 = ((16 * -3 + -10x * -3) + x(16 + -10x))
-6 + 19x + 1x2 = ((-48 + 30x) + x(16 + -10x))
-6 + 19x + 1x2 = (-48 + 30x + (16 * x + -10x * x))
-6 + 19x + 1x2 = (-48 + 30x + (16x + -10x2))

Combine like terms: 30x + 16x = 46x
-6 + 19x + 1x2 = (-48 + 46x + -10x2)

Solving
-6 + 19x + 1x2 = -48 + 46x + -10x2

Solving for variable 'x'.

Reorder the terms:
-6 + 48 + 19x + -46x + 1x2 + 10x2 = -48 + 46x + -10x2 + 48 + -46x + 10x2

Combine like terms: -6 + 48 = 42
42 + 19x + -46x + 1x2 + 10x2 = -48 + 46x + -10x2 + 48 + -46x + 10x2

Combine like terms: 19x + -46x = -27x
42 + -27x + 1x2 + 10x2 = -48 + 46x + -10x2 + 48 + -46x + 10x2

Combine like terms: 1x2 + 10x2 = 11x2
42 + -27x + 11x2 = -48 + 46x + -10x2 + 48 + -46x + 10x2

Reorder the terms:
42 + -27x + 11x2 = -48 + 48 + 46x + -46x + -10x2 + 10x2

Combine like terms: -48 + 48 = 0
42 + -27x + 11x2 = 0 + 46x + -46x + -10x2 + 10x2
42 + -27x + 11x2 = 46x + -46x + -10x2 + 10x2

Combine like terms: 46x + -46x = 0
42 + -27x + 11x2 = 0 + -10x2 + 10x2
42 + -27x + 11x2 = -10x2 + 10x2

Combine like terms: -10x2 + 10x2 = 0
42 + -27x + 11x2 = 0

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

Divide each side by '11'.
3.818181818 + -2.454545455x + x2 = 0

Move the constant term to the right:

Add '-3.818181818' to each side of the equation.
3.818181818 + -2.454545455x + -3.818181818 + x2 = 0 + -3.818181818

Reorder the terms:
3.818181818 + -3.818181818 + -2.454545455x + x2 = 0 + -3.818181818

Combine like terms: 3.818181818 + -3.818181818 = 0.000000000
0.000000000 + -2.454545455x + x2 = 0 + -3.818181818
-2.454545455x + x2 = 0 + -3.818181818

Combine like terms: 0 + -3.818181818 = -3.818181818
-2.454545455x + x2 = -3.818181818

The x term is -2.454545455x.  Take half its coefficient (-1.227272728).
Square it (1.506198349) and add it to both sides.

Add '1.506198349' to each side of the equation.
-2.454545455x + 1.506198349 + x2 = -3.818181818 + 1.506198349

Reorder the terms:
1.506198349 + -2.454545455x + x2 = -3.818181818 + 1.506198349

Combine like terms: -3.818181818 + 1.506198349 = -2.311983469
1.506198349 + -2.454545455x + x2 = -2.311983469

Factor a perfect square on the left side:
(x + -1.227272728)(x + -1.227272728) = -2.311983469

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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