(x+3)2x+8=42

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

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

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

Reorder the terms for easier multiplication:
2x(3 + x) + 8 = 42
(3 * 2x + x * 2x) + 8 = 42
(6x + 2x2) + 8 = 42

Reorder the terms:
8 + 6x + 2x2 = 42

Solving
8 + 6x + 2x2 = 42

Solving for variable 'x'.

Reorder the terms:
8 + -42 + 6x + 2x2 = 42 + -42

Combine like terms: 8 + -42 = -34
-34 + 6x + 2x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-34 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + 3x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-17 + 3x + x2 = 0

Solving
-17 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 3x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + 3x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 3x + x2 = 0 + 17
3x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
3x + x2 = 17

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 17 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 17 + 2.25

Combine like terms: 17 + 2.25 = 19.25
2.25 + 3x + x2 = 19.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(x + 1.5) equal to 4.387482194 and -4.387482194.

Subproblem 1
x + 1.5 = 4.387482194

Simplifying
x + 1.5 = 4.387482194

Reorder the terms:
1.5 + x = 4.387482194

Solving
1.5 + x = 4.387482194

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 4.387482194 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 4.387482194 + -1.5
x = 4.387482194 + -1.5

Combine like terms: 4.387482194 + -1.5 = 2.887482194
x = 2.887482194

Simplifying
x = 2.887482194

Subproblem 2
x + 1.5 = -4.387482194

Simplifying
x + 1.5 = -4.387482194

Reorder the terms:
1.5 + x = -4.387482194

Solving
1.5 + x = -4.387482194

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -4.387482194 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -4.387482194 + -1.5
x = -4.387482194 + -1.5

Combine like terms: -4.387482194 + -1.5 = -5.887482194
x = -5.887482194

Simplifying
x = -5.887482194

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.887482194, -5.887482194}
Solution
x = {2.887482194, -5.887482194}