(0.5x+4)(2x+6)-17=39-(x-1)(8-x)

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Solution for (0.5x+4)(2x+6)-17=39-(x-1)(8-x) equation: 


Simplifying
(0.5x + 4)(2x + 6) + -17 = 39 + -1(x + -1)(8 + -1x)

Reorder the terms:
(4 + 0.5x)(2x + 6) + -17 = 39 + -1(x + -1)(8 + -1x)

Reorder the terms:
(4 + 0.5x)(6 + 2x) + -17 = 39 + -1(x + -1)(8 + -1x)

Multiply (4 + 0.5x) * (6 + 2x)
(4(6 + 2x) + 0.5x * (6 + 2x)) + -17 = 39 + -1(x + -1)(8 + -1x)
((6 * 4 + 2x * 4) + 0.5x * (6 + 2x)) + -17 = 39 + -1(x + -1)(8 + -1x)
((24 + 8x) + 0.5x * (6 + 2x)) + -17 = 39 + -1(x + -1)(8 + -1x)
(24 + 8x + (6 * 0.5x + 2x * 0.5x)) + -17 = 39 + -1(x + -1)(8 + -1x)
(24 + 8x + (3x + 1x2)) + -17 = 39 + -1(x + -1)(8 + -1x)

Combine like terms: 8x + 3x = 11x
(24 + 11x + 1x2) + -17 = 39 + -1(x + -1)(8 + -1x)

Reorder the terms:
24 + -17 + 11x + 1x2 = 39 + -1(x + -1)(8 + -1x)

Combine like terms: 24 + -17 = 7
7 + 11x + 1x2 = 39 + -1(x + -1)(8 + -1x)

Reorder the terms:
7 + 11x + 1x2 = 39 + -1(-1 + x)(8 + -1x)

Multiply (-1 + x) * (8 + -1x)
7 + 11x + 1x2 = 39 + -1(-1(8 + -1x) + x(8 + -1x))
7 + 11x + 1x2 = 39 + -1((8 * -1 + -1x * -1) + x(8 + -1x))
7 + 11x + 1x2 = 39 + -1((-8 + 1x) + x(8 + -1x))
7 + 11x + 1x2 = 39 + -1(-8 + 1x + (8 * x + -1x * x))
7 + 11x + 1x2 = 39 + -1(-8 + 1x + (8x + -1x2))

Combine like terms: 1x + 8x = 9x
7 + 11x + 1x2 = 39 + -1(-8 + 9x + -1x2)
7 + 11x + 1x2 = 39 + (-8 * -1 + 9x * -1 + -1x2 * -1)
7 + 11x + 1x2 = 39 + (8 + -9x + 1x2)

Combine like terms: 39 + 8 = 47
7 + 11x + 1x2 = 47 + -9x + 1x2

Add '-1x2' to each side of the equation.
7 + 11x + 1x2 + -1x2 = 47 + -9x + 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
7 + 11x + 0 = 47 + -9x + 1x2 + -1x2
7 + 11x = 47 + -9x + 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
7 + 11x = 47 + -9x + 0
7 + 11x = 47 + -9x

Solving
7 + 11x = 47 + -9x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '9x' to each side of the equation.
7 + 11x + 9x = 47 + -9x + 9x

Combine like terms: 11x + 9x = 20x
7 + 20x = 47 + -9x + 9x

Combine like terms: -9x + 9x = 0
7 + 20x = 47 + 0
7 + 20x = 47

Add '-7' to each side of the equation.
7 + -7 + 20x = 47 + -7

Combine like terms: 7 + -7 = 0
0 + 20x = 47 + -7
20x = 47 + -7

Combine like terms: 47 + -7 = 40
20x = 40

Divide each side by '20'.
x = 2

Simplifying
x = 2

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