3(x-2)=-2x(x+19)

Solution for 3(x-2)=-2x(x+19) equation:

Simplifying
3(x + -2) = -2x(x + 19)

Reorder the terms:
3(-2 + x) = -2x(x + 19)
(-2 * 3 + x * 3) = -2x(x + 19)
(-6 + 3x) = -2x(x + 19)

Reorder the terms:
-6 + 3x = -2x(19 + x)
-6 + 3x = (19 * -2x + x * -2x)
-6 + 3x = (-38x + -2x2)

Solving
-6 + 3x = -38x + -2x2

Solving for variable 'x'.

Combine like terms: 3x + 38x = 41x
-6 + 41x + 2x2 = -38x + -2x2 + 38x + 2x2

Reorder the terms:
-6 + 41x + 2x2 = -38x + 38x + -2x2 + 2x2

Combine like terms: -38x + 38x = 0
-6 + 41x + 2x2 = 0 + -2x2 + 2x2
-6 + 41x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-6 + 41x + 2x2 = 0

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

Divide each side by '2'.
-3 + 20.5x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 20.5x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 20.5x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 20.5x + x2 = 0 + 3
20.5x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
20.5x + x2 = 3

The x term is 20.5x.  Take half its coefficient (10.25).
Square it (105.0625) and add it to both sides.

Add '105.0625' to each side of the equation.
20.5x + 105.0625 + x2 = 3 + 105.0625

Reorder the terms:
105.0625 + 20.5x + x2 = 3 + 105.0625

Combine like terms: 3 + 105.0625 = 108.0625
105.0625 + 20.5x + x2 = 108.0625

Factor a perfect square on the left side:
(x + 10.25)(x + 10.25) = 108.0625

Calculate the square root of the right side: 10.395311443

Break this problem into two subproblems by setting 
(x + 10.25) equal to 10.395311443 and -10.395311443.

Subproblem 1
x + 10.25 = 10.395311443

Simplifying
x + 10.25 = 10.395311443

Reorder the terms:
10.25 + x = 10.395311443

Solving
10.25 + x = 10.395311443

Solving for variable 'x'.

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

Add '-10.25' to each side of the equation.
10.25 + -10.25 + x = 10.395311443 + -10.25

Combine like terms: 10.25 + -10.25 = 0.00
0.00 + x = 10.395311443 + -10.25
x = 10.395311443 + -10.25

Combine like terms: 10.395311443 + -10.25 = 0.145311443
x = 0.145311443

Simplifying
x = 0.145311443

Subproblem 2
x + 10.25 = -10.395311443

Simplifying
x + 10.25 = -10.395311443

Reorder the terms:
10.25 + x = -10.395311443

Solving
10.25 + x = -10.395311443

Solving for variable 'x'.

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

Add '-10.25' to each side of the equation.
10.25 + -10.25 + x = -10.395311443 + -10.25

Combine like terms: 10.25 + -10.25 = 0.00
0.00 + x = -10.395311443 + -10.25
x = -10.395311443 + -10.25

Combine like terms: -10.395311443 + -10.25 = -20.645311443
x = -20.645311443

Simplifying
x = -20.645311443

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.145311443, -20.645311443}