2x*(x+37)=42

Solution for 2x*(x+37)=42 equation:

Simplifying
2x(x + 37) = 42

Reorder the terms:
2x(37 + x) = 42
(37 * 2x + x * 2x) = 42
(74x + 2x2) = 42

Solving
74x + 2x2 = 42

Solving for variable 'x'.

Reorder the terms:
-42 + 74x + 2x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + 74x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 37x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-21 + 37x + x2)' equal to zero and attempt to solve:

Simplifying
-21 + 37x + x2 = 0

Solving
-21 + 37x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 37x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 37x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 37x + x2 = 0 + 21
37x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
37x + x2 = 21

The x term is 37x.  Take half its coefficient (18.5).
Square it (342.25) and add it to both sides.

Add '342.25' to each side of the equation.
37x + 342.25 + x2 = 21 + 342.25

Reorder the terms:
342.25 + 37x + x2 = 21 + 342.25

Combine like terms: 21 + 342.25 = 363.25
342.25 + 37x + x2 = 363.25

Factor a perfect square on the left side:
(x + 18.5)(x + 18.5) = 363.25

Calculate the square root of the right side: 19.059118553

Break this problem into two subproblems by setting 
(x + 18.5) equal to 19.059118553 and -19.059118553.

Subproblem 1
x + 18.5 = 19.059118553

Simplifying
x + 18.5 = 19.059118553

Reorder the terms:
18.5 + x = 19.059118553

Solving
18.5 + x = 19.059118553

Solving for variable 'x'.

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

Add '-18.5' to each side of the equation.
18.5 + -18.5 + x = 19.059118553 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + x = 19.059118553 + -18.5
x = 19.059118553 + -18.5

Combine like terms: 19.059118553 + -18.5 = 0.559118553
x = 0.559118553

Simplifying
x = 0.559118553

Subproblem 2
x + 18.5 = -19.059118553

Simplifying
x + 18.5 = -19.059118553

Reorder the terms:
18.5 + x = -19.059118553

Solving
18.5 + x = -19.059118553

Solving for variable 'x'.

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

Add '-18.5' to each side of the equation.
18.5 + -18.5 + x = -19.059118553 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + x = -19.059118553 + -18.5
x = -19.059118553 + -18.5

Combine like terms: -19.059118553 + -18.5 = -37.559118553
x = -37.559118553

Simplifying
x = -37.559118553

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.559118553, -37.559118553}
Solution
x = {0.559118553, -37.559118553}