4x(x-3)=64

Solution for 4x(x-3)=64 equation:

Simplifying
4x(x + -3) = 64

Reorder the terms:
4x(-3 + x) = 64
(-3 * 4x + x * 4x) = 64
(-12x + 4x2) = 64

Solving
-12x + 4x2 = 64

Solving for variable 'x'.

Reorder the terms:
-64 + -12x + 4x2 = 64 + -64

Combine like terms: 64 + -64 = 0
-64 + -12x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + -3x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-16 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
-16 + -3x + x2 = 0

Solving
-16 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -3x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -3x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -3x + x2 = 0 + 16
-3x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-3x + x2 = 16

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 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 16 + 2.25

Combine like terms: 16 + 2.25 = 18.25
2.25 + -3x + x2 = 18.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + -1.5) equal to 4.272001873 and -4.272001873.

Subproblem 1
x + -1.5 = 4.272001873

Simplifying
x + -1.5 = 4.272001873

Reorder the terms:
-1.5 + x = 4.272001873

Solving
-1.5 + x = 4.272001873

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 = 4.272001873 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 4.272001873 + 1.5
x = 4.272001873 + 1.5

Combine like terms: 4.272001873 + 1.5 = 5.772001873
x = 5.772001873

Simplifying
x = 5.772001873

Subproblem 2
x + -1.5 = -4.272001873

Simplifying
x + -1.5 = -4.272001873

Reorder the terms:
-1.5 + x = -4.272001873

Solving
-1.5 + x = -4.272001873

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 = -4.272001873 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -4.272001873 + 1.5
x = -4.272001873 + 1.5

Combine like terms: -4.272001873 + 1.5 = -2.772001873
x = -2.772001873

Simplifying
x = -2.772001873

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.772001873, -2.772001873}
Solution
x = {5.772001873, -2.772001873}