4(x+3)=2x(x-6)

Solution for 4(x+3)=2x(x-6) equation:

Simplifying
4(x + 3) = 2x(x + -6)

Reorder the terms:
4(3 + x) = 2x(x + -6)
(3 * 4 + x * 4) = 2x(x + -6)
(12 + 4x) = 2x(x + -6)

Reorder the terms:
12 + 4x = 2x(-6 + x)
12 + 4x = (-6 * 2x + x * 2x)
12 + 4x = (-12x + 2x2)

Solving
12 + 4x = -12x + 2x2

Solving for variable 'x'.

Combine like terms: 4x + 12x = 16x
12 + 16x + -2x2 = -12x + 2x2 + 12x + -2x2

Reorder the terms:
12 + 16x + -2x2 = -12x + 12x + 2x2 + -2x2

Combine like terms: -12x + 12x = 0
12 + 16x + -2x2 = 0 + 2x2 + -2x2
12 + 16x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
12 + 16x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 8x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + 8x + -1x2)' equal to zero and attempt to solve:

Simplifying
6 + 8x + -1x2 = 0

Solving
6 + 8x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + -8x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -8x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -8x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -8x + x2 = 0 + 6
-8x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-8x + x2 = 6

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 6 + 16

Reorder the terms:
16 + -8x + x2 = 6 + 16

Combine like terms: 6 + 16 = 22
16 + -8x + x2 = 22

Factor a perfect square on the left side:
(x + -4)(x + -4) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(x + -4) equal to 4.69041576 and -4.69041576.

Subproblem 1
x + -4 = 4.69041576

Simplifying
x + -4 = 4.69041576

Reorder the terms:
-4 + x = 4.69041576

Solving
-4 + x = 4.69041576

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 4.69041576 + 4

Combine like terms: -4 + 4 = 0
0 + x = 4.69041576 + 4
x = 4.69041576 + 4

Combine like terms: 4.69041576 + 4 = 8.69041576
x = 8.69041576

Simplifying
x = 8.69041576

Subproblem 2
x + -4 = -4.69041576

Simplifying
x + -4 = -4.69041576

Reorder the terms:
-4 + x = -4.69041576

Solving
-4 + x = -4.69041576

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -4.69041576 + 4

Combine like terms: -4 + 4 = 0
0 + x = -4.69041576 + 4
x = -4.69041576 + 4

Combine like terms: -4.69041576 + 4 = -0.69041576
x = -0.69041576

Simplifying
x = -0.69041576

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.69041576, -0.69041576}
Solution
x = {8.69041576, -0.69041576}