(x+4)(2x+6)=30

Solution for (x+4)(2x+6)=30 equation:

Simplifying
(x + 4)(2x + 6) = 30

Reorder the terms:
(4 + x)(2x + 6) = 30

Reorder the terms:
(4 + x)(6 + 2x) = 30

Multiply (4 + x) * (6 + 2x)
(4(6 + 2x) + x(6 + 2x)) = 30
((6 * 4 + 2x * 4) + x(6 + 2x)) = 30
((24 + 8x) + x(6 + 2x)) = 30
(24 + 8x + (6 * x + 2x * x)) = 30
(24 + 8x + (6x + 2x2)) = 30

Combine like terms: 8x + 6x = 14x
(24 + 14x + 2x2) = 30

Solving
24 + 14x + 2x2 = 30

Solving for variable 'x'.

Reorder the terms:
24 + -30 + 14x + 2x2 = 30 + -30

Combine like terms: 24 + -30 = -6
-6 + 14x + 2x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-6 + 14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 7x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 7x + x2)' equal to zero and attempt to solve:

Simplifying
-3 + 7x + x2 = 0

Solving
-3 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 7x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 7x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 7x + x2 = 0 + 3
7x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
7x + x2 = 3

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 3 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 3 + 12.25

Combine like terms: 3 + 12.25 = 15.25
12.25 + 7x + x2 = 15.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.905124838 and -3.905124838.

Subproblem 1
x + 3.5 = 3.905124838

Simplifying
x + 3.5 = 3.905124838

Reorder the terms:
3.5 + x = 3.905124838

Solving
3.5 + x = 3.905124838

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 3.905124838 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 3.905124838 + -3.5
x = 3.905124838 + -3.5

Combine like terms: 3.905124838 + -3.5 = 0.405124838
x = 0.405124838

Simplifying
x = 0.405124838

Subproblem 2
x + 3.5 = -3.905124838

Simplifying
x + 3.5 = -3.905124838

Reorder the terms:
3.5 + x = -3.905124838

Solving
3.5 + x = -3.905124838

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -3.905124838 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -3.905124838 + -3.5
x = -3.905124838 + -3.5

Combine like terms: -3.905124838 + -3.5 = -7.405124838
x = -7.405124838

Simplifying
x = -7.405124838

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.405124838, -7.405124838}
Solution
x = {0.405124838, -7.405124838}