3x(2x+6)=100

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Solution for 3x(2x+6)=100 equation: 


Simplifying
3x(2x + 6) = 100

Reorder the terms:
3x(6 + 2x) = 100
(6 * 3x + 2x * 3x) = 100
(18x + 6x2) = 100

Solving
18x + 6x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + 18x + 6x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 18x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 9x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-50 + 9x + 3x2)' equal to zero and attempt to solve:

Simplifying
-50 + 9x + 3x2 = 0

Solving
-50 + 9x + 3x2 = 0

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

Divide each side by '3'.
-16.66666667 + 3x + x2 = 0

Move the constant term to the right:

Add '16.66666667' to each side of the equation.
-16.66666667 + 3x + 16.66666667 + x2 = 0 + 16.66666667

Reorder the terms:
-16.66666667 + 16.66666667 + 3x + x2 = 0 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + 3x + x2 = 0 + 16.66666667
3x + x2 = 0 + 16.66666667

Combine like terms: 0 + 16.66666667 = 16.66666667
3x + x2 = 16.66666667

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 16.66666667 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 16.66666667 + 2.25

Combine like terms: 16.66666667 + 2.25 = 18.91666667
2.25 + 3x + x2 = 18.91666667

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 18.91666667

Calculate the square root of the right side: 4.349329451

Break this problem into two subproblems by setting 
(x + 1.5) equal to 4.349329451 and -4.349329451.


Subproblem 1
x + 1.5 = 4.349329451

Simplifying
x + 1.5 = 4.349329451

Reorder the terms:
1.5 + x = 4.349329451

Solving
1.5 + x = 4.349329451

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 4.349329451 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 4.349329451 + -1.5
x = 4.349329451 + -1.5

Combine like terms: 4.349329451 + -1.5 = 2.849329451
x = 2.849329451

Simplifying
x = 2.849329451


Subproblem 2
x + 1.5 = -4.349329451

Simplifying
x + 1.5 = -4.349329451

Reorder the terms:
1.5 + x = -4.349329451

Solving
1.5 + x = -4.349329451

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -4.349329451 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -4.349329451 + -1.5
x = -4.349329451 + -1.5

Combine like terms: -4.349329451 + -1.5 = -5.849329451
x = -5.849329451

Simplifying
x = -5.849329451


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.849329451, -5.849329451}
Solution
x = {2.849329451, -5.849329451}

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