4(-2x+9)=3x(2x+12)

Solution for 4(-2x+9)=3x(2x+12) equation:

Simplifying
4(-2x + 9) = 3x(2x + 12)

Reorder the terms:
4(9 + -2x) = 3x(2x + 12)
(9 * 4 + -2x * 4) = 3x(2x + 12)
(36 + -8x) = 3x(2x + 12)

Reorder the terms:
36 + -8x = 3x(12 + 2x)
36 + -8x = (12 * 3x + 2x * 3x)
36 + -8x = (36x + 6x2)

Solving
36 + -8x = 36x + 6x2

Solving for variable 'x'.

Combine like terms: -8x + -36x = -44x
36 + -44x + -6x2 = 36x + 6x2 + -36x + -6x2

Reorder the terms:
36 + -44x + -6x2 = 36x + -36x + 6x2 + -6x2

Combine like terms: 36x + -36x = 0
36 + -44x + -6x2 = 0 + 6x2 + -6x2
36 + -44x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
36 + -44x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + -22x + -3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(18 + -22x + -3x2)' equal to zero and attempt to solve:

Simplifying
18 + -22x + -3x2 = 0

Solving
18 + -22x + -3x2 = 0

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

Divide each side by '-3'.
-6 + 7.333333333x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 7.333333333x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 7.333333333x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 7.333333333x + x2 = 0 + 6
7.333333333x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
7.333333333x + x2 = 6

The x term is 7.333333333x.  Take half its coefficient (3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
7.333333333x + 13.44444445 + x2 = 6 + 13.44444445

Reorder the terms:
13.44444445 + 7.333333333x + x2 = 6 + 13.44444445

Combine like terms: 6 + 13.44444445 = 19.44444445
13.44444445 + 7.333333333x + x2 = 19.44444445

Factor a perfect square on the left side:
(x + 3.666666667)(x + 3.666666667) = 19.44444445

Calculate the square root of the right side: 4.409585519

Break this problem into two subproblems by setting 
(x + 3.666666667) equal to 4.409585519 and -4.409585519.

Subproblem 1
x + 3.666666667 = 4.409585519

Simplifying
x + 3.666666667 = 4.409585519

Reorder the terms:
3.666666667 + x = 4.409585519

Solving
3.666666667 + x = 4.409585519

Solving for variable 'x'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + x = 4.409585519 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + x = 4.409585519 + -3.666666667
x = 4.409585519 + -3.666666667

Combine like terms: 4.409585519 + -3.666666667 = 0.742918852
x = 0.742918852

Simplifying
x = 0.742918852

Subproblem 2
x + 3.666666667 = -4.409585519

Simplifying
x + 3.666666667 = -4.409585519

Reorder the terms:
3.666666667 + x = -4.409585519

Solving
3.666666667 + x = -4.409585519

Solving for variable 'x'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + x = -4.409585519 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + x = -4.409585519 + -3.666666667
x = -4.409585519 + -3.666666667

Combine like terms: -4.409585519 + -3.666666667 = -8.076252186
x = -8.076252186

Simplifying
x = -8.076252186

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.742918852, -8.076252186}
Solution
x = {0.742918852, -8.076252186}