(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 + -17 + 2x) = 39 + -1(x + -1)(8 + -1x)

Combine like terms: 6 + -17 = -11
(4 + 0.5x)(-11 + 2x) = 39 + -1(x + -1)(8 + -1x)

Multiply (4 + 0.5x) * (-11 + 2x)
(4(-11 + 2x) + 0.5x * (-11 + 2x)) = 39 + -1(x + -1)(8 + -1x)
((-11 * 4 + 2x * 4) + 0.5x * (-11 + 2x)) = 39 + -1(x + -1)(8 + -1x)
((-44 + 8x) + 0.5x * (-11 + 2x)) = 39 + -1(x + -1)(8 + -1x)
(-44 + 8x + (-11 * 0.5x + 2x * 0.5x)) = 39 + -1(x + -1)(8 + -1x)
(-44 + 8x + (-5.5x + 1x2)) = 39 + -1(x + -1)(8 + -1x)

Combine like terms: 8x + -5.5x = 2.5x
(-44 + 2.5x + 1x2) = 39 + -1(x + -1)(8 + -1x)

Reorder the terms:
-44 + 2.5x + 1x2 = 39 + -1(-1 + x)(8 + -1x)

Multiply (-1 + x) * (8 + -1x)
-44 + 2.5x + 1x2 = 39 + -1(-1(8 + -1x) + x(8 + -1x))
-44 + 2.5x + 1x2 = 39 + -1((8 * -1 + -1x * -1) + x(8 + -1x))
-44 + 2.5x + 1x2 = 39 + -1((-8 + 1x) + x(8 + -1x))
-44 + 2.5x + 1x2 = 39 + -1(-8 + 1x + (8 * x + -1x * x))
-44 + 2.5x + 1x2 = 39 + -1(-8 + 1x + (8x + -1x2))

Combine like terms: 1x + 8x = 9x
-44 + 2.5x + 1x2 = 39 + -1(-8 + 9x + -1x2)
-44 + 2.5x + 1x2 = 39 + (-8 * -1 + 9x * -1 + -1x2 * -1)
-44 + 2.5x + 1x2 = 39 + (8 + -9x + 1x2)

Combine like terms: 39 + 8 = 47
-44 + 2.5x + 1x2 = 47 + -9x + 1x2

Add '-1x2' to each side of the equation.
-44 + 2.5x + 1x2 + -1x2 = 47 + -9x + 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-44 + 2.5x + 0 = 47 + -9x + 1x2 + -1x2
-44 + 2.5x = 47 + -9x + 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-44 + 2.5x = 47 + -9x + 0
-44 + 2.5x = 47 + -9x

Solving
-44 + 2.5x = 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.
-44 + 2.5x + 9x = 47 + -9x + 9x

Combine like terms: 2.5x + 9x = 11.5x
-44 + 11.5x = 47 + -9x + 9x

Combine like terms: -9x + 9x = 0
-44 + 11.5x = 47 + 0
-44 + 11.5x = 47

Add '44' to each side of the equation.
-44 + 44 + 11.5x = 47 + 44

Combine like terms: -44 + 44 = 0
0 + 11.5x = 47 + 44
11.5x = 47 + 44

Combine like terms: 47 + 44 = 91
11.5x = 91

Divide each side by '11.5'.
x = 7.913043478

Simplifying
x = 7.913043478

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