(.5)(2x+4)(x+3)=56

Solution for (.5)(2x+4)(x+3)=56 equation:

Simplifying
(0.5)(2x + 4)(x + 3) = 56

Reorder the terms:
0.5(4 + 2x)(x + 3) = 56

Reorder the terms:
0.5(4 + 2x)(3 + x) = 56

Multiply (4 + 2x) * (3 + x)
0.5(4(3 + x) + 2x * (3 + x)) = 56
0.5((3 * 4 + x * 4) + 2x * (3 + x)) = 56
0.5((12 + 4x) + 2x * (3 + x)) = 56
0.5(12 + 4x + (3 * 2x + x * 2x)) = 56
0.5(12 + 4x + (6x + 2x2)) = 56

Combine like terms: 4x + 6x = 10x
0.5(12 + 10x + 2x2) = 56
(12 * 0.5 + 10x * 0.5 + 2x2 * 0.5) = 56
(6 + 5x + 1x2) = 56

Solving
6 + 5x + 1x2 = 56

Solving for variable 'x'.

Reorder the terms:
6 + -56 + 5x + 1x2 = 56 + -56

Combine like terms: 6 + -56 = -50
-50 + 5x + 1x2 = 56 + -56

Combine like terms: 56 + -56 = 0
-50 + 5x + 1x2 = 0

Factor a trinomial.
(-10 + -1x)(5 + -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 '(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
Solution
x = {-10, 5}