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

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

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

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

Reorder the terms:
-6x + -3x2 = -8(-8 + -3x)
-6x + -3x2 = (-8 * -8 + -3x * -8)
-6x + -3x2 = (64 + 24x)

Solving
-6x + -3x2 = 64 + 24x

Solving for variable 'x'.

Reorder the terms:
-64 + -6x + -24x + -3x2 = 64 + 24x + -64 + -24x

Combine like terms: -6x + -24x = -30x
-64 + -30x + -3x2 = 64 + 24x + -64 + -24x

Reorder the terms:
-64 + -30x + -3x2 = 64 + -64 + 24x + -24x

Combine like terms: 64 + -64 = 0
-64 + -30x + -3x2 = 0 + 24x + -24x
-64 + -30x + -3x2 = 24x + -24x

Combine like terms: 24x + -24x = 0
-64 + -30x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(64 + 30x + 3x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(64 + 30x + 3x2)' equal to zero and attempt to solve:

Simplifying
64 + 30x + 3x2 = 0

Solving
64 + 30x + 3x2 = 0

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

Divide each side by '3'.
21.33333333 + 10x + x2 = 0

Move the constant term to the right:

Add '-21.33333333' to each side of the equation.
21.33333333 + 10x + -21.33333333 + x2 = 0 + -21.33333333

Reorder the terms:
21.33333333 + -21.33333333 + 10x + x2 = 0 + -21.33333333

Combine like terms: 21.33333333 + -21.33333333 = 0.00000000
0.00000000 + 10x + x2 = 0 + -21.33333333
10x + x2 = 0 + -21.33333333

Combine like terms: 0 + -21.33333333 = -21.33333333
10x + x2 = -21.33333333

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -21.33333333 + 25

Reorder the terms:
25 + 10x + x2 = -21.33333333 + 25

Combine like terms: -21.33333333 + 25 = 3.66666667
25 + 10x + x2 = 3.66666667

Factor a perfect square on the left side:
(x + 5)(x + 5) = 3.66666667

Calculate the square root of the right side: 1.914854216

Break this problem into two subproblems by setting 
(x + 5) equal to 1.914854216 and -1.914854216.

Subproblem 1
x + 5 = 1.914854216

Simplifying
x + 5 = 1.914854216

Reorder the terms:
5 + x = 1.914854216

Solving
5 + x = 1.914854216

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 1.914854216 + -5

Combine like terms: 5 + -5 = 0
0 + x = 1.914854216 + -5
x = 1.914854216 + -5

Combine like terms: 1.914854216 + -5 = -3.085145784
x = -3.085145784

Simplifying
x = -3.085145784

Subproblem 2
x + 5 = -1.914854216

Simplifying
x + 5 = -1.914854216

Reorder the terms:
5 + x = -1.914854216

Solving
5 + x = -1.914854216

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -1.914854216 + -5

Combine like terms: 5 + -5 = 0
0 + x = -1.914854216 + -5
x = -1.914854216 + -5

Combine like terms: -1.914854216 + -5 = -6.914854216
x = -6.914854216

Simplifying
x = -6.914854216

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.085145784, -6.914854216}
Solution
x = {-3.085145784, -6.914854216}