2x(3x-3)+7(5+6x)=

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Solution for 2x(3x-3)+7(5+6x)= equation: 


Simplifying
2x(3x + -3) + 7(5 + 6x) = 0

Reorder the terms:
2x(-3 + 3x) + 7(5 + 6x) = 0
(-3 * 2x + 3x * 2x) + 7(5 + 6x) = 0
(-6x + 6x2) + 7(5 + 6x) = 0
-6x + 6x2 + (5 * 7 + 6x * 7) = 0
-6x + 6x2 + (35 + 42x) = 0

Reorder the terms:
35 + -6x + 42x + 6x2 = 0

Combine like terms: -6x + 42x = 36x
35 + 36x + 6x2 = 0

Solving
35 + 36x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
5.833333333 + 6x + x2 = 0

Move the constant term to the right:

Add '-5.833333333' to each side of the equation.
5.833333333 + 6x + -5.833333333 + x2 = 0 + -5.833333333

Reorder the terms:
5.833333333 + -5.833333333 + 6x + x2 = 0 + -5.833333333

Combine like terms: 5.833333333 + -5.833333333 = 0.000000000
0.000000000 + 6x + x2 = 0 + -5.833333333
6x + x2 = 0 + -5.833333333

Combine like terms: 0 + -5.833333333 = -5.833333333
6x + x2 = -5.833333333

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -5.833333333 + 9

Reorder the terms:
9 + 6x + x2 = -5.833333333 + 9

Combine like terms: -5.833333333 + 9 = 3.166666667
9 + 6x + x2 = 3.166666667

Factor a perfect square on the left side:
(x + 3)(x + 3) = 3.166666667

Calculate the square root of the right side: 1.779513042

Break this problem into two subproblems by setting 
(x + 3) equal to 1.779513042 and -1.779513042.


Subproblem 1
x + 3 = 1.779513042

Simplifying
x + 3 = 1.779513042

Reorder the terms:
3 + x = 1.779513042

Solving
3 + x = 1.779513042

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 1.779513042 + -3

Combine like terms: 3 + -3 = 0
0 + x = 1.779513042 + -3
x = 1.779513042 + -3

Combine like terms: 1.779513042 + -3 = -1.220486958
x = -1.220486958

Simplifying
x = -1.220486958


Subproblem 2
x + 3 = -1.779513042

Simplifying
x + 3 = -1.779513042

Reorder the terms:
3 + x = -1.779513042

Solving
3 + x = -1.779513042

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -1.779513042 + -3

Combine like terms: 3 + -3 = 0
0 + x = -1.779513042 + -3
x = -1.779513042 + -3

Combine like terms: -1.779513042 + -3 = -4.779513042
x = -4.779513042

Simplifying
x = -4.779513042


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.220486958, -4.779513042}

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