(0.5x+3)(8x-2)-(2x-6)(4+2x)=12(x+4)

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Solution for (0.5x+3)(8x-2)-(2x-6)(4+2x)=12(x+4) equation: 


Simplifying
(0.5x + 3)(8x + -2) + -1(2x + -6)(4 + 2x) = 12(x + 4)

Reorder the terms:
(3 + 0.5x)(8x + -2) + -1(2x + -6)(4 + 2x) = 12(x + 4)

Reorder the terms:
(3 + 0.5x)(-2 + 8x) + -1(2x + -6)(4 + 2x) = 12(x + 4)

Multiply (3 + 0.5x) * (-2 + 8x)
(3(-2 + 8x) + 0.5x * (-2 + 8x)) + -1(2x + -6)(4 + 2x) = 12(x + 4)
((-2 * 3 + 8x * 3) + 0.5x * (-2 + 8x)) + -1(2x + -6)(4 + 2x) = 12(x + 4)
((-6 + 24x) + 0.5x * (-2 + 8x)) + -1(2x + -6)(4 + 2x) = 12(x + 4)
(-6 + 24x + (-2 * 0.5x + 8x * 0.5x)) + -1(2x + -6)(4 + 2x) = 12(x + 4)
(-6 + 24x + (-1x + 4x2)) + -1(2x + -6)(4 + 2x) = 12(x + 4)

Combine like terms: 24x + -1x = 23x
(-6 + 23x + 4x2) + -1(2x + -6)(4 + 2x) = 12(x + 4)

Reorder the terms:
-6 + 23x + 4x2 + -1(-6 + 2x)(4 + 2x) = 12(x + 4)

Multiply (-6 + 2x) * (4 + 2x)
-6 + 23x + 4x2 + -1(-6(4 + 2x) + 2x * (4 + 2x)) = 12(x + 4)
-6 + 23x + 4x2 + -1((4 * -6 + 2x * -6) + 2x * (4 + 2x)) = 12(x + 4)
-6 + 23x + 4x2 + -1((-24 + -12x) + 2x * (4 + 2x)) = 12(x + 4)
-6 + 23x + 4x2 + -1(-24 + -12x + (4 * 2x + 2x * 2x)) = 12(x + 4)
-6 + 23x + 4x2 + -1(-24 + -12x + (8x + 4x2)) = 12(x + 4)

Combine like terms: -12x + 8x = -4x
-6 + 23x + 4x2 + -1(-24 + -4x + 4x2) = 12(x + 4)
-6 + 23x + 4x2 + (-24 * -1 + -4x * -1 + 4x2 * -1) = 12(x + 4)
-6 + 23x + 4x2 + (24 + 4x + -4x2) = 12(x + 4)

Reorder the terms:
-6 + 24 + 23x + 4x + 4x2 + -4x2 = 12(x + 4)

Combine like terms: -6 + 24 = 18
18 + 23x + 4x + 4x2 + -4x2 = 12(x + 4)

Combine like terms: 23x + 4x = 27x
18 + 27x + 4x2 + -4x2 = 12(x + 4)

Combine like terms: 4x2 + -4x2 = 0
18 + 27x + 0 = 12(x + 4)
18 + 27x = 12(x + 4)

Reorder the terms:
18 + 27x = 12(4 + x)
18 + 27x = (4 * 12 + x * 12)
18 + 27x = (48 + 12x)

Solving
18 + 27x = 48 + 12x

Solving for variable 'x'.

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

Add '-12x' to each side of the equation.
18 + 27x + -12x = 48 + 12x + -12x

Combine like terms: 27x + -12x = 15x
18 + 15x = 48 + 12x + -12x

Combine like terms: 12x + -12x = 0
18 + 15x = 48 + 0
18 + 15x = 48

Add '-18' to each side of the equation.
18 + -18 + 15x = 48 + -18

Combine like terms: 18 + -18 = 0
0 + 15x = 48 + -18
15x = 48 + -18

Combine like terms: 48 + -18 = 30
15x = 30

Divide each side by '15'.
x = 2

Simplifying
x = 2

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