3x(3x-1)=4(3+3x)

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


Simplifying
3x(3x + -1) = 4(3 + 3x)

Reorder the terms:
3x(-1 + 3x) = 4(3 + 3x)
(-1 * 3x + 3x * 3x) = 4(3 + 3x)
(-3x + 9x2) = 4(3 + 3x)
-3x + 9x2 = (3 * 4 + 3x * 4)
-3x + 9x2 = (12 + 12x)

Solving
-3x + 9x2 = 12 + 12x

Solving for variable 'x'.

Reorder the terms:
-12 + -3x + -12x + 9x2 = 12 + 12x + -12 + -12x

Combine like terms: -3x + -12x = -15x
-12 + -15x + 9x2 = 12 + 12x + -12 + -12x

Reorder the terms:
-12 + -15x + 9x2 = 12 + -12 + 12x + -12x

Combine like terms: 12 + -12 = 0
-12 + -15x + 9x2 = 0 + 12x + -12x
-12 + -15x + 9x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-12 + -15x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + -5x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + -5x + 3x2)' equal to zero and attempt to solve:

Simplifying
-4 + -5x + 3x2 = 0

Solving
-4 + -5x + 3x2 = 0

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

Divide each side by '3'.
-1.333333333 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -1.666666667x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -1.666666667x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -1.666666667x + x2 = 0 + 1.333333333
-1.666666667x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-1.666666667x + x2 = 1.333333333

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = 1.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = 1.333333333 + 0.6944444447

Combine like terms: 1.333333333 + 0.6944444447 = 2.0277777777
0.6944444447 + -1.666666667x + x2 = 2.0277777777

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 2.0277777777

Calculate the square root of the right side: 1.424000624

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 1.424000624 and -1.424000624.


Subproblem 1
x + -0.8333333335 = 1.424000624

Simplifying
x + -0.8333333335 = 1.424000624

Reorder the terms:
-0.8333333335 + x = 1.424000624

Solving
-0.8333333335 + x = 1.424000624

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = 1.424000624 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 1.424000624 + 0.8333333335
x = 1.424000624 + 0.8333333335

Combine like terms: 1.424000624 + 0.8333333335 = 2.2573339575
x = 2.2573339575

Simplifying
x = 2.2573339575


Subproblem 2
x + -0.8333333335 = -1.424000624

Simplifying
x + -0.8333333335 = -1.424000624

Reorder the terms:
-0.8333333335 + x = -1.424000624

Solving
-0.8333333335 + x = -1.424000624

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = -1.424000624 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -1.424000624 + 0.8333333335
x = -1.424000624 + 0.8333333335

Combine like terms: -1.424000624 + 0.8333333335 = -0.5906672905
x = -0.5906672905

Simplifying
x = -0.5906672905


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.2573339575, -0.5906672905}
Solution
x = {2.2573339575, -0.5906672905}

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