42=.5(2x+8)(x+3)

Solution for 42=.5(2x+8)(x+3) equation:

Simplifying
42 = 0.5(2x + 8)(x + 3)

Reorder the terms:
42 = 0.5(8 + 2x)(x + 3)

Reorder the terms:
42 = 0.5(8 + 2x)(3 + x)

Multiply (8 + 2x) * (3 + x)
42 = 0.5(8(3 + x) + 2x * (3 + x))
42 = 0.5((3 * 8 + x * 8) + 2x * (3 + x))
42 = 0.5((24 + 8x) + 2x * (3 + x))
42 = 0.5(24 + 8x + (3 * 2x + x * 2x))
42 = 0.5(24 + 8x + (6x + 2x2))

Combine like terms: 8x + 6x = 14x
42 = 0.5(24 + 14x + 2x2)
42 = (24 * 0.5 + 14x * 0.5 + 2x2 * 0.5)
42 = (12 + 7x + 1x2)

Solving
42 = 12 + 7x + 1x2

Solving for variable 'x'.

Combine like terms: 42 + -12 = 30
30 + -7x + -1x2 = 12 + 7x + 1x2 + -12 + -7x + -1x2

Reorder the terms:
30 + -7x + -1x2 = 12 + -12 + 7x + -7x + 1x2 + -1x2

Combine like terms: 12 + -12 = 0
30 + -7x + -1x2 = 0 + 7x + -7x + 1x2 + -1x2
30 + -7x + -1x2 = 7x + -7x + 1x2 + -1x2

Combine like terms: 7x + -7x = 0
30 + -7x + -1x2 = 0 + 1x2 + -1x2
30 + -7x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
30 + -7x + -1x2 = 0

Factor a trinomial.
(3 + -1x)(10 + 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 '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Solution
x = {3, -10}