42=(2x)(x+9)

Solution for 42=(2x)(x+9) equation:

Simplifying
42 = (2x)(x + 9)

Remove parenthesis around (2x)
42 = 2x(x + 9)

Reorder the terms:
42 = 2x(9 + x)
42 = (9 * 2x + x * 2x)
42 = (18x + 2x2)

Solving
42 = 18x + 2x2

Solving for variable 'x'.

Reorder the terms:
42 + -18x + -2x2 = 18x + -18x + 2x2 + -2x2

Combine like terms: 18x + -18x = 0
42 + -18x + -2x2 = 0 + 2x2 + -2x2
42 + -18x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
42 + -18x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + -9x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(21 + -9x + -1x2)' equal to zero and attempt to solve:

Simplifying
21 + -9x + -1x2 = 0

Solving
21 + -9x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-21 + 9x + x2 = 0

Move the constant term to the right:

Add '21' to each side of the equation.
-21 + 9x + 21 + x2 = 0 + 21

Reorder the terms:
-21 + 21 + 9x + x2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 9x + x2 = 0 + 21
9x + x2 = 0 + 21

Combine like terms: 0 + 21 = 21
9x + x2 = 21

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 21 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 21 + 20.25

Combine like terms: 21 + 20.25 = 41.25
20.25 + 9x + x2 = 41.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 41.25

Calculate the square root of the right side: 6.422616289

Break this problem into two subproblems by setting 
(x + 4.5) equal to 6.422616289 and -6.422616289.

Subproblem 1
x + 4.5 = 6.422616289

Simplifying
x + 4.5 = 6.422616289

Reorder the terms:
4.5 + x = 6.422616289

Solving
4.5 + x = 6.422616289

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 6.422616289 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 6.422616289 + -4.5
x = 6.422616289 + -4.5

Combine like terms: 6.422616289 + -4.5 = 1.922616289
x = 1.922616289

Simplifying
x = 1.922616289

Subproblem 2
x + 4.5 = -6.422616289

Simplifying
x + 4.5 = -6.422616289

Reorder the terms:
4.5 + x = -6.422616289

Solving
4.5 + x = -6.422616289

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -6.422616289 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -6.422616289 + -4.5
x = -6.422616289 + -4.5

Combine like terms: -6.422616289 + -4.5 = -10.922616289
x = -10.922616289

Simplifying
x = -10.922616289

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.922616289, -10.922616289}
Solution
x = {1.922616289, -10.922616289}