(4+6x)(3+x)+5(3x+x)=

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Solution for (4+6x)(3+x)+5(3x+x)= equation: 


Simplifying
(4 + 6x)(3 + x) + 5(3x + x) = 0

Multiply (4 + 6x) * (3 + x)
(4(3 + x) + 6x * (3 + x)) + 5(3x + x) = 0
((3 * 4 + x * 4) + 6x * (3 + x)) + 5(3x + x) = 0
((12 + 4x) + 6x * (3 + x)) + 5(3x + x) = 0
(12 + 4x + (3 * 6x + x * 6x)) + 5(3x + x) = 0
(12 + 4x + (18x + 6x2)) + 5(3x + x) = 0

Combine like terms: 4x + 18x = 22x
(12 + 22x + 6x2) + 5(3x + x) = 0

Combine like terms: 3x + x = 4x
12 + 22x + 6x2 + 5(4x) = 0

Remove parenthesis around (4x)
12 + 22x + 6x2 + 5 * 4x = 0

Multiply 5 * 4
12 + 22x + 6x2 + 20x = 0

Reorder the terms:
12 + 22x + 20x + 6x2 = 0

Combine like terms: 22x + 20x = 42x
12 + 42x + 6x2 = 0

Solving
12 + 42x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(2 + 7x + x2) = 0

Ignore the factor 6.

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

Simplifying
2 + 7x + x2 = 0

Solving
2 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 7x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 7x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7x + x2 = 0 + -2
7x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
7x + x2 = -2

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 = -2 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -2 + 12.25

Combine like terms: -2 + 12.25 = 10.25
12.25 + 7x + x2 = 10.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.201562119 and -3.201562119.


Subproblem 1
x + 3.5 = 3.201562119

Simplifying
x + 3.5 = 3.201562119

Reorder the terms:
3.5 + x = 3.201562119

Solving
3.5 + x = 3.201562119

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 = 3.201562119 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 3.201562119 + -3.5
x = 3.201562119 + -3.5

Combine like terms: 3.201562119 + -3.5 = -0.298437881
x = -0.298437881

Simplifying
x = -0.298437881


Subproblem 2
x + 3.5 = -3.201562119

Simplifying
x + 3.5 = -3.201562119

Reorder the terms:
3.5 + x = -3.201562119

Solving
3.5 + x = -3.201562119

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 = -3.201562119 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -3.201562119 + -3.5
x = -3.201562119 + -3.5

Combine like terms: -3.201562119 + -3.5 = -6.701562119
x = -6.701562119

Simplifying
x = -6.701562119


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.298437881, -6.701562119}
Solution
x = {-0.298437881, -6.701562119}

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