9x(5x+12)=12

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Solution for 9x(5x+12)=12 equation: 


Simplifying
9x(5x + 12) = 12

Reorder the terms:
9x(12 + 5x) = 12
(12 * 9x + 5x * 9x) = 12
(108x + 45x2) = 12

Solving
108x + 45x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + 108x + 45x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 108x + 45x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 36x + 15x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + 36x + 15x2)' equal to zero and attempt to solve:

Simplifying
-4 + 36x + 15x2 = 0

Solving
-4 + 36x + 15x2 = 0

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

Divide each side by '15'.
-0.2666666667 + 2.4x + x2 = 0

Move the constant term to the right:

Add '0.2666666667' to each side of the equation.
-0.2666666667 + 2.4x + 0.2666666667 + x2 = 0 + 0.2666666667

Reorder the terms:
-0.2666666667 + 0.2666666667 + 2.4x + x2 = 0 + 0.2666666667

Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000
0.0000000000 + 2.4x + x2 = 0 + 0.2666666667
2.4x + x2 = 0 + 0.2666666667

Combine like terms: 0 + 0.2666666667 = 0.2666666667
2.4x + x2 = 0.2666666667

The x term is 2.4x.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4x + 1.44 + x2 = 0.2666666667 + 1.44

Reorder the terms:
1.44 + 2.4x + x2 = 0.2666666667 + 1.44

Combine like terms: 0.2666666667 + 1.44 = 1.7066666667
1.44 + 2.4x + x2 = 1.7066666667

Factor a perfect square on the left side:
(x + 1.2)(x + 1.2) = 1.7066666667

Calculate the square root of the right side: 1.306394529

Break this problem into two subproblems by setting 
(x + 1.2) equal to 1.306394529 and -1.306394529.


Subproblem 1
x + 1.2 = 1.306394529

Simplifying
x + 1.2 = 1.306394529

Reorder the terms:
1.2 + x = 1.306394529

Solving
1.2 + x = 1.306394529

Solving for variable 'x'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + x = 1.306394529 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + x = 1.306394529 + -1.2
x = 1.306394529 + -1.2

Combine like terms: 1.306394529 + -1.2 = 0.106394529
x = 0.106394529

Simplifying
x = 0.106394529


Subproblem 2
x + 1.2 = -1.306394529

Simplifying
x + 1.2 = -1.306394529

Reorder the terms:
1.2 + x = -1.306394529

Solving
1.2 + x = -1.306394529

Solving for variable 'x'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + x = -1.306394529 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + x = -1.306394529 + -1.2
x = -1.306394529 + -1.2

Combine like terms: -1.306394529 + -1.2 = -2.506394529
x = -2.506394529

Simplifying
x = -2.506394529


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.106394529, -2.506394529}
Solution
x = {0.106394529, -2.506394529}

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