3x-5x(x+4)=2(x-7)

Solution for 3x-5x(x+4)=2(x-7) equation:

Simplifying
3x + -5x(x + 4) = 2(x + -7)

Reorder the terms:
3x + -5x(4 + x) = 2(x + -7)
3x + (4 * -5x + x * -5x) = 2(x + -7)
3x + (-20x + -5x2) = 2(x + -7)

Combine like terms: 3x + -20x = -17x
-17x + -5x2 = 2(x + -7)

Reorder the terms:
-17x + -5x2 = 2(-7 + x)
-17x + -5x2 = (-7 * 2 + x * 2)
-17x + -5x2 = (-14 + 2x)

Solving
-17x + -5x2 = -14 + 2x

Solving for variable 'x'.

Reorder the terms:
14 + -17x + -2x + -5x2 = -14 + 2x + 14 + -2x

Combine like terms: -17x + -2x = -19x
14 + -19x + -5x2 = -14 + 2x + 14 + -2x

Reorder the terms:
14 + -19x + -5x2 = -14 + 14 + 2x + -2x

Combine like terms: -14 + 14 = 0
14 + -19x + -5x2 = 0 + 2x + -2x
14 + -19x + -5x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
14 + -19x + -5x2 = 0

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

Divide each side by '-5'.
-2.8 + 3.8x + x2 = 0

Move the constant term to the right:

Add '2.8' to each side of the equation.
-2.8 + 3.8x + 2.8 + x2 = 0 + 2.8

Reorder the terms:
-2.8 + 2.8 + 3.8x + x2 = 0 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + 3.8x + x2 = 0 + 2.8
3.8x + x2 = 0 + 2.8

Combine like terms: 0 + 2.8 = 2.8
3.8x + x2 = 2.8

The x term is 3.8x.  Take half its coefficient (1.9).
Square it (3.61) and add it to both sides.

Add '3.61' to each side of the equation.
3.8x + 3.61 + x2 = 2.8 + 3.61

Reorder the terms:
3.61 + 3.8x + x2 = 2.8 + 3.61

Combine like terms: 2.8 + 3.61 = 6.41
3.61 + 3.8x + x2 = 6.41

Factor a perfect square on the left side:
(x + 1.9)(x + 1.9) = 6.41

Calculate the square root of the right side: 2.53179778

Break this problem into two subproblems by setting 
(x + 1.9) equal to 2.53179778 and -2.53179778.

Subproblem 1
x + 1.9 = 2.53179778

Simplifying
x + 1.9 = 2.53179778

Reorder the terms:
1.9 + x = 2.53179778

Solving
1.9 + x = 2.53179778

Solving for variable 'x'.

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

Add '-1.9' to each side of the equation.
1.9 + -1.9 + x = 2.53179778 + -1.9

Combine like terms: 1.9 + -1.9 = 0.0
0.0 + x = 2.53179778 + -1.9
x = 2.53179778 + -1.9

Combine like terms: 2.53179778 + -1.9 = 0.63179778
x = 0.63179778

Simplifying
x = 0.63179778

Subproblem 2
x + 1.9 = -2.53179778

Simplifying
x + 1.9 = -2.53179778

Reorder the terms:
1.9 + x = -2.53179778

Solving
1.9 + x = -2.53179778

Solving for variable 'x'.

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

Add '-1.9' to each side of the equation.
1.9 + -1.9 + x = -2.53179778 + -1.9

Combine like terms: 1.9 + -1.9 = 0.0
0.0 + x = -2.53179778 + -1.9
x = -2.53179778 + -1.9

Combine like terms: -2.53179778 + -1.9 = -4.43179778
x = -4.43179778

Simplifying
x = -4.43179778

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.63179778, -4.43179778}