2x(x-8)=3(x+3)

Solution for 2x(x-8)=3(x+3) equation:

Simplifying
2x(x + -8) = 3(x + 3)

Reorder the terms:
2x(-8 + x) = 3(x + 3)
(-8 * 2x + x * 2x) = 3(x + 3)
(-16x + 2x2) = 3(x + 3)

Reorder the terms:
-16x + 2x2 = 3(3 + x)
-16x + 2x2 = (3 * 3 + x * 3)
-16x + 2x2 = (9 + 3x)

Solving
-16x + 2x2 = 9 + 3x

Solving for variable 'x'.

Reorder the terms:
-9 + -16x + -3x + 2x2 = 9 + 3x + -9 + -3x

Combine like terms: -16x + -3x = -19x
-9 + -19x + 2x2 = 9 + 3x + -9 + -3x

Reorder the terms:
-9 + -19x + 2x2 = 9 + -9 + 3x + -3x

Combine like terms: 9 + -9 = 0
-9 + -19x + 2x2 = 0 + 3x + -3x
-9 + -19x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-9 + -19x + 2x2 = 0

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

Divide each side by '2'.
-4.5 + -9.5x + x2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -9.5x + 4.5 + x2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -9.5x + x2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -9.5x + x2 = 0 + 4.5
-9.5x + x2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-9.5x + x2 = 4.5

The x term is -9.5x.  Take half its coefficient (-4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
-9.5x + 22.5625 + x2 = 4.5 + 22.5625

Reorder the terms:
22.5625 + -9.5x + x2 = 4.5 + 22.5625

Combine like terms: 4.5 + 22.5625 = 27.0625
22.5625 + -9.5x + x2 = 27.0625

Factor a perfect square on the left side:
(x + -4.75)(x + -4.75) = 27.0625

Calculate the square root of the right side: 5.202163012

Break this problem into two subproblems by setting 
(x + -4.75) equal to 5.202163012 and -5.202163012.

Subproblem 1
x + -4.75 = 5.202163012

Simplifying
x + -4.75 = 5.202163012

Reorder the terms:
-4.75 + x = 5.202163012

Solving
-4.75 + x = 5.202163012

Solving for variable 'x'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + x = 5.202163012 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + x = 5.202163012 + 4.75
x = 5.202163012 + 4.75

Combine like terms: 5.202163012 + 4.75 = 9.952163012
x = 9.952163012

Simplifying
x = 9.952163012

Subproblem 2
x + -4.75 = -5.202163012

Simplifying
x + -4.75 = -5.202163012

Reorder the terms:
-4.75 + x = -5.202163012

Solving
-4.75 + x = -5.202163012

Solving for variable 'x'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + x = -5.202163012 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + x = -5.202163012 + 4.75
x = -5.202163012 + 4.75

Combine like terms: -5.202163012 + 4.75 = -0.452163012
x = -0.452163012

Simplifying
x = -0.452163012

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.952163012, -0.452163012}