50=.5(2x+14)(x+2)

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Solution for 50=.5(2x+14)(x+2) equation: 


Simplifying
50 = 0.5(2x + 14)(x + 2)

Reorder the terms:
50 = 0.5(14 + 2x)(x + 2)

Reorder the terms:
50 = 0.5(14 + 2x)(2 + x)

Multiply (14 + 2x) * (2 + x)
50 = 0.5(14(2 + x) + 2x * (2 + x))
50 = 0.5((2 * 14 + x * 14) + 2x * (2 + x))
50 = 0.5((28 + 14x) + 2x * (2 + x))
50 = 0.5(28 + 14x + (2 * 2x + x * 2x))
50 = 0.5(28 + 14x + (4x + 2x2))

Combine like terms: 14x + 4x = 18x
50 = 0.5(28 + 18x + 2x2)
50 = (28 * 0.5 + 18x * 0.5 + 2x2 * 0.5)
50 = (14 + 9x + 1x2)

Solving
50 = 14 + 9x + 1x2

Solving for variable 'x'.

Combine like terms: 50 + -14 = 36
36 + -9x + -1x2 = 14 + 9x + 1x2 + -14 + -9x + -1x2

Reorder the terms:
36 + -9x + -1x2 = 14 + -14 + 9x + -9x + 1x2 + -1x2

Combine like terms: 14 + -14 = 0
36 + -9x + -1x2 = 0 + 9x + -9x + 1x2 + -1x2
36 + -9x + -1x2 = 9x + -9x + 1x2 + -1x2

Combine like terms: 9x + -9x = 0
36 + -9x + -1x2 = 0 + 1x2 + -1x2
36 + -9x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
36 + -9x + -1x2 = 0

Factor a trinomial.
(3 + -1x)(12 + x) = 0


Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Solution
x = {3, -12}

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