84=.5(x+7)(2x+4)

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Solution for 84=.5(x+7)(2x+4) equation: 


Simplifying
84 = 0.5(x + 7)(2x + 4)

Reorder the terms:
84 = 0.5(7 + x)(2x + 4)

Reorder the terms:
84 = 0.5(7 + x)(4 + 2x)

Multiply (7 + x) * (4 + 2x)
84 = 0.5(7(4 + 2x) + x(4 + 2x))
84 = 0.5((4 * 7 + 2x * 7) + x(4 + 2x))
84 = 0.5((28 + 14x) + x(4 + 2x))
84 = 0.5(28 + 14x + (4 * x + 2x * x))
84 = 0.5(28 + 14x + (4x + 2x2))

Combine like terms: 14x + 4x = 18x
84 = 0.5(28 + 18x + 2x2)
84 = (28 * 0.5 + 18x * 0.5 + 2x2 * 0.5)
84 = (14 + 9x + 1x2)

Solving
84 = 14 + 9x + 1x2

Solving for variable 'x'.

Combine like terms: 84 + -14 = 70
70 + -9x + -1x2 = 14 + 9x + 1x2 + -14 + -9x + -1x2

Reorder the terms:
70 + -9x + -1x2 = 14 + -14 + 9x + -9x + 1x2 + -1x2

Combine like terms: 14 + -14 = 0
70 + -9x + -1x2 = 0 + 9x + -9x + 1x2 + -1x2
70 + -9x + -1x2 = 9x + -9x + 1x2 + -1x2

Combine like terms: 9x + -9x = 0
70 + -9x + -1x2 = 0 + 1x2 + -1x2
70 + -9x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
70 + -9x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(14 + x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(14 + x)' equal to zero and attempt to solve:

Simplifying
14 + x = 0

Solving
14 + x = 0

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

Add '-14' to each side of the equation.
14 + -14 + x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + x = 0 + -14
x = 0 + -14

Combine like terms: 0 + -14 = -14
x = -14

Simplifying
x = -14
Solution
x = {5, -14}

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