4(x+5)=3x(x-2)-2(x+2)

Solution for 4(x+5)=3x(x-2)-2(x+2) equation:

Simplifying
4(x + 5) = 3x(x + -2) + -2(x + 2)

Reorder the terms:
4(5 + x) = 3x(x + -2) + -2(x + 2)
(5 * 4 + x * 4) = 3x(x + -2) + -2(x + 2)
(20 + 4x) = 3x(x + -2) + -2(x + 2)

Reorder the terms:
20 + 4x = 3x(-2 + x) + -2(x + 2)
20 + 4x = (-2 * 3x + x * 3x) + -2(x + 2)
20 + 4x = (-6x + 3x2) + -2(x + 2)

Reorder the terms:
20 + 4x = -6x + 3x2 + -2(2 + x)
20 + 4x = -6x + 3x2 + (2 * -2 + x * -2)
20 + 4x = -6x + 3x2 + (-4 + -2x)

Reorder the terms:
20 + 4x = -4 + -6x + -2x + 3x2

Combine like terms: -6x + -2x = -8x
20 + 4x = -4 + -8x + 3x2

Solving
20 + 4x = -4 + -8x + 3x2

Solving for variable 'x'.

Reorder the terms:
20 + 4 + 4x + 8x + -3x2 = -4 + -8x + 3x2 + 4 + 8x + -3x2

Combine like terms: 20 + 4 = 24
24 + 4x + 8x + -3x2 = -4 + -8x + 3x2 + 4 + 8x + -3x2

Combine like terms: 4x + 8x = 12x
24 + 12x + -3x2 = -4 + -8x + 3x2 + 4 + 8x + -3x2

Reorder the terms:
24 + 12x + -3x2 = -4 + 4 + -8x + 8x + 3x2 + -3x2

Combine like terms: -4 + 4 = 0
24 + 12x + -3x2 = 0 + -8x + 8x + 3x2 + -3x2
24 + 12x + -3x2 = -8x + 8x + 3x2 + -3x2

Combine like terms: -8x + 8x = 0
24 + 12x + -3x2 = 0 + 3x2 + -3x2
24 + 12x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
24 + 12x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + 4x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(8 + 4x + -1x2)' equal to zero and attempt to solve:

Simplifying
8 + 4x + -1x2 = 0

Solving
8 + 4x + -1x2 = 0

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

Divide each side by '-1'.
-8 + -4x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -4x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -4x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -4x + x2 = 0 + 8
-4x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-4x + x2 = 8

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 8 + 4

Reorder the terms:
4 + -4x + x2 = 8 + 4

Combine like terms: 8 + 4 = 12
4 + -4x + x2 = 12

Factor a perfect square on the left side:
(x + -2)(x + -2) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + -2) equal to 3.464101615 and -3.464101615.

Subproblem 1
x + -2 = 3.464101615

Simplifying
x + -2 = 3.464101615

Reorder the terms:
-2 + x = 3.464101615

Solving
-2 + x = 3.464101615

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 3.464101615 + 2

Combine like terms: -2 + 2 = 0
0 + x = 3.464101615 + 2
x = 3.464101615 + 2

Combine like terms: 3.464101615 + 2 = 5.464101615
x = 5.464101615

Simplifying
x = 5.464101615

Subproblem 2
x + -2 = -3.464101615

Simplifying
x + -2 = -3.464101615

Reorder the terms:
-2 + x = -3.464101615

Solving
-2 + x = -3.464101615

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -3.464101615 + 2

Combine like terms: -2 + 2 = 0
0 + x = -3.464101615 + 2
x = -3.464101615 + 2

Combine like terms: -3.464101615 + 2 = -1.464101615
x = -1.464101615

Simplifying
x = -1.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.464101615, -1.464101615}
Solution
x = {5.464101615, -1.464101615}