4x(3x+3)+7(6x+1)=

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Solution for 4x(3x+3)+7(6x+1)= equation: 


Simplifying
4x(3x + 3) + 7(6x + 1) = 0

Reorder the terms:
4x(3 + 3x) + 7(6x + 1) = 0
(3 * 4x + 3x * 4x) + 7(6x + 1) = 0
(12x + 12x2) + 7(6x + 1) = 0

Reorder the terms:
12x + 12x2 + 7(1 + 6x) = 0
12x + 12x2 + (1 * 7 + 6x * 7) = 0
12x + 12x2 + (7 + 42x) = 0

Reorder the terms:
7 + 12x + 42x + 12x2 = 0

Combine like terms: 12x + 42x = 54x
7 + 54x + 12x2 = 0

Solving
7 + 54x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
0.5833333333 + 4.5x + x2 = 0

Move the constant term to the right:

Add '-0.5833333333' to each side of the equation.
0.5833333333 + 4.5x + -0.5833333333 + x2 = 0 + -0.5833333333

Reorder the terms:
0.5833333333 + -0.5833333333 + 4.5x + x2 = 0 + -0.5833333333

Combine like terms: 0.5833333333 + -0.5833333333 = 0.0000000000
0.0000000000 + 4.5x + x2 = 0 + -0.5833333333
4.5x + x2 = 0 + -0.5833333333

Combine like terms: 0 + -0.5833333333 = -0.5833333333
4.5x + x2 = -0.5833333333

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = -0.5833333333 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = -0.5833333333 + 5.0625

Combine like terms: -0.5833333333 + 5.0625 = 4.4791666667
5.0625 + 4.5x + x2 = 4.4791666667

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 4.4791666667

Calculate the square root of the right side: 2.116404183

Break this problem into two subproblems by setting 
(x + 2.25) equal to 2.116404183 and -2.116404183.


Subproblem 1
x + 2.25 = 2.116404183

Simplifying
x + 2.25 = 2.116404183

Reorder the terms:
2.25 + x = 2.116404183

Solving
2.25 + x = 2.116404183

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = 2.116404183 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 2.116404183 + -2.25
x = 2.116404183 + -2.25

Combine like terms: 2.116404183 + -2.25 = -0.133595817
x = -0.133595817

Simplifying
x = -0.133595817


Subproblem 2
x + 2.25 = -2.116404183

Simplifying
x + 2.25 = -2.116404183

Reorder the terms:
2.25 + x = -2.116404183

Solving
2.25 + x = -2.116404183

Solving for variable 'x'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + x = -2.116404183 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -2.116404183 + -2.25
x = -2.116404183 + -2.25

Combine like terms: -2.116404183 + -2.25 = -4.366404183
x = -4.366404183

Simplifying
x = -4.366404183


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.133595817, -4.366404183}

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