(2+8)*(x-3)=(x+6)*(2x-4)

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Solution for (2+8)*(x-3)=(x+6)*(2x-4) equation: 


Simplifying
(2 + 8)(x + -3) = (x + 6)(2x + -4)

Combine like terms: 2 + 8 = 10
(10)(x + -3) = (x + 6)(2x + -4)

Reorder the terms:
10(-3 + x) = (x + 6)(2x + -4)
(-3 * 10 + x * 10) = (x + 6)(2x + -4)
(-30 + 10x) = (x + 6)(2x + -4)

Reorder the terms:
-30 + 10x = (6 + x)(2x + -4)

Reorder the terms:
-30 + 10x = (6 + x)(-4 + 2x)

Multiply (6 + x) * (-4 + 2x)
-30 + 10x = (6(-4 + 2x) + x(-4 + 2x))
-30 + 10x = ((-4 * 6 + 2x * 6) + x(-4 + 2x))
-30 + 10x = ((-24 + 12x) + x(-4 + 2x))
-30 + 10x = (-24 + 12x + (-4 * x + 2x * x))
-30 + 10x = (-24 + 12x + (-4x + 2x2))

Combine like terms: 12x + -4x = 8x
-30 + 10x = (-24 + 8x + 2x2)

Solving
-30 + 10x = -24 + 8x + 2x2

Solving for variable 'x'.

Reorder the terms:
-30 + 24 + 10x + -8x + -2x2 = -24 + 8x + 2x2 + 24 + -8x + -2x2

Combine like terms: -30 + 24 = -6
-6 + 10x + -8x + -2x2 = -24 + 8x + 2x2 + 24 + -8x + -2x2

Combine like terms: 10x + -8x = 2x
-6 + 2x + -2x2 = -24 + 8x + 2x2 + 24 + -8x + -2x2

Reorder the terms:
-6 + 2x + -2x2 = -24 + 24 + 8x + -8x + 2x2 + -2x2

Combine like terms: -24 + 24 = 0
-6 + 2x + -2x2 = 0 + 8x + -8x + 2x2 + -2x2
-6 + 2x + -2x2 = 8x + -8x + 2x2 + -2x2

Combine like terms: 8x + -8x = 0
-6 + 2x + -2x2 = 0 + 2x2 + -2x2
-6 + 2x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-6 + 2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + x + -1x2)' equal to zero and attempt to solve:

Simplifying
-3 + x + -1x2 = 0

Solving
-3 + x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
3 + -1x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -1x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -1x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x + x2 = 0 + -3
-1x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x + x2 = -3

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -3 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -3 + 0.25

Combine like terms: -3 + 0.25 = -2.75
0.25 + -1x + x2 = -2.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -2.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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