30=0.5(2x+8)(x+3)

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Solution for 30=0.5(2x+8)(x+3) equation: 


Simplifying
30 = 0.5(2x + 8)(x + 3)

Reorder the terms:
30 = 0.5(8 + 2x)(x + 3)

Reorder the terms:
30 = 0.5(8 + 2x)(3 + x)

Multiply (8 + 2x) * (3 + x)
30 = 0.5(8(3 + x) + 2x * (3 + x))
30 = 0.5((3 * 8 + x * 8) + 2x * (3 + x))
30 = 0.5((24 + 8x) + 2x * (3 + x))
30 = 0.5(24 + 8x + (3 * 2x + x * 2x))
30 = 0.5(24 + 8x + (6x + 2x2))

Combine like terms: 8x + 6x = 14x
30 = 0.5(24 + 14x + 2x2)
30 = (24 * 0.5 + 14x * 0.5 + 2x2 * 0.5)
30 = (12 + 7x + 1x2)

Solving
30 = 12 + 7x + 1x2

Solving for variable 'x'.

Combine like terms: 30 + -12 = 18
18 + -7x + -1x2 = 12 + 7x + 1x2 + -12 + -7x + -1x2

Reorder the terms:
18 + -7x + -1x2 = 12 + -12 + 7x + -7x + 1x2 + -1x2

Combine like terms: 12 + -12 = 0
18 + -7x + -1x2 = 0 + 7x + -7x + 1x2 + -1x2
18 + -7x + -1x2 = 7x + -7x + 1x2 + -1x2

Combine like terms: 7x + -7x = 0
18 + -7x + -1x2 = 0 + 1x2 + -1x2
18 + -7x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
18 + -7x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(9 + x) = 0


Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9
Solution
x = {2, -9}

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