2x(6+3x)=33

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Solution for 2x(6+3x)=33 equation:


Simplifying
2x(6 + 3x) = 33
(6 * 2x + 3x * 2x) = 33
(12x + 6x2) = 33

Solving
12x + 6x2 = 33

Solving for variable 'x'.

Reorder the terms:
-33 + 12x + 6x2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + 12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-11 + 4x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-11 + 4x + 2x2)' equal to zero and attempt to solve:

Simplifying
-11 + 4x + 2x2 = 0

Solving
-11 + 4x + 2x2 = 0

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

Divide each side by '2'.
-5.5 + 2x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + 2x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + 2x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + 2x + x2 = 0 + 5.5
2x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
2x + x2 = 5.5

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 5.5 + 1

Reorder the terms:
1 + 2x + x2 = 5.5 + 1

Combine like terms: 5.5 + 1 = 6.5
1 + 2x + x2 = 6.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = 6.5

Calculate the square root of the right side: 2.549509757

Break this problem into two subproblems by setting 
(x + 1) equal to 2.549509757 and -2.549509757.


Subproblem 1
x + 1 = 2.549509757

Simplifying
x + 1 = 2.549509757

Reorder the terms:
1 + x = 2.549509757

Solving
1 + x = 2.549509757

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 2.549509757 + -1

Combine like terms: 1 + -1 = 0
0 + x = 2.549509757 + -1
x = 2.549509757 + -1

Combine like terms: 2.549509757 + -1 = 1.549509757
x = 1.549509757

Simplifying
x = 1.549509757


Subproblem 2
x + 1 = -2.549509757

Simplifying
x + 1 = -2.549509757

Reorder the terms:
1 + x = -2.549509757

Solving
1 + x = -2.549509757

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -2.549509757 + -1

Combine like terms: 1 + -1 = 0
0 + x = -2.549509757 + -1
x = -2.549509757 + -1

Combine like terms: -2.549509757 + -1 = -3.549509757
x = -3.549509757

Simplifying
x = -3.549509757


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.549509757, -3.549509757}
Solution
x = {1.549509757, -3.549509757}

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