3(2x-4)=3x-5x(x+1)

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Solution for 3(2x-4)=3x-5x(x+1) equation: 


Simplifying
3(2x + -4) = 3x + -5x(x + 1)

Reorder the terms:
3(-4 + 2x) = 3x + -5x(x + 1)
(-4 * 3 + 2x * 3) = 3x + -5x(x + 1)
(-12 + 6x) = 3x + -5x(x + 1)

Reorder the terms:
-12 + 6x = 3x + -5x(1 + x)
-12 + 6x = 3x + (1 * -5x + x * -5x)
-12 + 6x = 3x + (-5x + -5x2)

Combine like terms: 3x + -5x = -2x
-12 + 6x = -2x + -5x2

Solving
-12 + 6x = -2x + -5x2

Solving for variable 'x'.

Combine like terms: 6x + 2x = 8x
-12 + 8x + 5x2 = -2x + -5x2 + 2x + 5x2

Reorder the terms:
-12 + 8x + 5x2 = -2x + 2x + -5x2 + 5x2

Combine like terms: -2x + 2x = 0
-12 + 8x + 5x2 = 0 + -5x2 + 5x2
-12 + 8x + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-12 + 8x + 5x2 = 0

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

Divide each side by '5'.
-2.4 + 1.6x + x2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + 1.6x + 2.4 + x2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + 1.6x + x2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + 1.6x + x2 = 0 + 2.4
1.6x + x2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
1.6x + x2 = 2.4

The x term is 1.6x.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6x + 0.64 + x2 = 2.4 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = 2.4 + 0.64

Combine like terms: 2.4 + 0.64 = 3.04
0.64 + 1.6x + x2 = 3.04

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = 3.04

Calculate the square root of the right side: 1.743559577

Break this problem into two subproblems by setting 
(x + 0.8) equal to 1.743559577 and -1.743559577.


Subproblem 1
x + 0.8 = 1.743559577

Simplifying
x + 0.8 = 1.743559577

Reorder the terms:
0.8 + x = 1.743559577

Solving
0.8 + x = 1.743559577

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = 1.743559577 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = 1.743559577 + -0.8
x = 1.743559577 + -0.8

Combine like terms: 1.743559577 + -0.8 = 0.943559577
x = 0.943559577

Simplifying
x = 0.943559577


Subproblem 2
x + 0.8 = -1.743559577

Simplifying
x + 0.8 = -1.743559577

Reorder the terms:
0.8 + x = -1.743559577

Solving
0.8 + x = -1.743559577

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = -1.743559577 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = -1.743559577 + -0.8
x = -1.743559577 + -0.8

Combine like terms: -1.743559577 + -0.8 = -2.543559577
x = -2.543559577

Simplifying
x = -2.543559577


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.943559577, -2.543559577}

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