20=0.5(2x+6)(x+2)

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Solution for 20=0.5(2x+6)(x+2) equation: 


Simplifying
20 = 0.5(2x + 6)(x + 2)

Reorder the terms:
20 = 0.5(6 + 2x)(x + 2)

Reorder the terms:
20 = 0.5(6 + 2x)(2 + x)

Multiply (6 + 2x) * (2 + x)
20 = 0.5(6(2 + x) + 2x * (2 + x))
20 = 0.5((2 * 6 + x * 6) + 2x * (2 + x))
20 = 0.5((12 + 6x) + 2x * (2 + x))
20 = 0.5(12 + 6x + (2 * 2x + x * 2x))
20 = 0.5(12 + 6x + (4x + 2x2))

Combine like terms: 6x + 4x = 10x
20 = 0.5(12 + 10x + 2x2)
20 = (12 * 0.5 + 10x * 0.5 + 2x2 * 0.5)
20 = (6 + 5x + 1x2)

Solving
20 = 6 + 5x + 1x2

Solving for variable 'x'.

Combine like terms: 20 + -6 = 14
14 + -5x + -1x2 = 6 + 5x + 1x2 + -6 + -5x + -1x2

Reorder the terms:
14 + -5x + -1x2 = 6 + -6 + 5x + -5x + 1x2 + -1x2

Combine like terms: 6 + -6 = 0
14 + -5x + -1x2 = 0 + 5x + -5x + 1x2 + -1x2
14 + -5x + -1x2 = 5x + -5x + 1x2 + -1x2

Combine like terms: 5x + -5x = 0
14 + -5x + -1x2 = 0 + 1x2 + -1x2
14 + -5x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
14 + -5x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(7 + 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 '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

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

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

Simplifying
x = -7
Solution
x = {2, -7}

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