(x+2)(3x+x)(.5)=140

Solution for (x+2)(3x+x)(.5)=140 equation:

Simplifying
(x + 2)(3x + x)(0.5) = 140

Reorder the terms:
(2 + x)(3x + x)(0.5) = 140

Combine like terms: 3x + x = 4x
(2 + x)(4x)(0.5) = 140

Remove parenthesis around (4x)
(2 + x) * 4x(0.5) = 140

Reorder the terms for easier multiplication:
4 * 0.5x(2 + x) = 140

Multiply 4 * 0.5
2x(2 + x) = 140
(2 * 2x + x * 2x) = 140
(4x + 2x2) = 140

Solving
4x + 2x2 = 140

Solving for variable 'x'.

Reorder the terms:
-140 + 4x + 2x2 = 140 + -140

Combine like terms: 140 + -140 = 0
-140 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-70 + 2x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-70 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-70 + 2x + x2 = 0

Solving
-70 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + 2x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + 2x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + 2x + x2 = 0 + 70
2x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
2x + x2 = 70

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 70 + 1

Reorder the terms:
1 + 2x + x2 = 70 + 1

Combine like terms: 70 + 1 = 71
1 + 2x + x2 = 71

Factor a perfect square on the left side:
(x + 1)(x + 1) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(x + 1) equal to 8.426149773 and -8.426149773.

Subproblem 1
x + 1 = 8.426149773

Simplifying
x + 1 = 8.426149773

Reorder the terms:
1 + x = 8.426149773

Solving
1 + x = 8.426149773

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 8.426149773 + -1

Combine like terms: 1 + -1 = 0
0 + x = 8.426149773 + -1
x = 8.426149773 + -1

Combine like terms: 8.426149773 + -1 = 7.426149773
x = 7.426149773

Simplifying
x = 7.426149773

Subproblem 2
x + 1 = -8.426149773

Simplifying
x + 1 = -8.426149773

Reorder the terms:
1 + x = -8.426149773

Solving
1 + x = -8.426149773

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -8.426149773 + -1

Combine like terms: 1 + -1 = 0
0 + x = -8.426149773 + -1
x = -8.426149773 + -1

Combine like terms: -8.426149773 + -1 = -9.426149773
x = -9.426149773

Simplifying
x = -9.426149773

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.426149773, -9.426149773}
Solution
x = {7.426149773, -9.426149773}