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

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

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

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

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

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

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

Solving
12 + 7x + 1x2 = 42

Solving for variable 'x'.

Reorder the terms:
12 + -42 + 7x + 1x2 = 42 + -42

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

Combine like terms: 42 + -42 = 0
-30 + 7x + 1x2 = 0

Factor a trinomial.
(-10 + -1x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 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 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10
Subproblem 2
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
Solution
x = {-10, 3}