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

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

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

Reorder the terms:
-5x(4 + x) = -2(2x + 1)
(4 * -5x + x * -5x) = -2(2x + 1)
(-20x + -5x2) = -2(2x + 1)

Reorder the terms:
-20x + -5x2 = -2(1 + 2x)
-20x + -5x2 = (1 * -2 + 2x * -2)
-20x + -5x2 = (-2 + -4x)

Solving
-20x + -5x2 = -2 + -4x

Solving for variable 'x'.

Reorder the terms:
2 + -20x + 4x + -5x2 = -2 + -4x + 2 + 4x

Combine like terms: -20x + 4x = -16x
2 + -16x + -5x2 = -2 + -4x + 2 + 4x

Reorder the terms:
2 + -16x + -5x2 = -2 + 2 + -4x + 4x

Combine like terms: -2 + 2 = 0
2 + -16x + -5x2 = 0 + -4x + 4x
2 + -16x + -5x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
2 + -16x + -5x2 = 0

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

Divide each side by '-5'.
-0.4 + 3.2x + x2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 3.2x + 0.4 + x2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 3.2x + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 3.2x + x2 = 0 + 0.4
3.2x + x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
3.2x + x2 = 0.4

The x term is 3.2x.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2x + 2.56 + x2 = 0.4 + 2.56

Reorder the terms:
2.56 + 3.2x + x2 = 0.4 + 2.56

Combine like terms: 0.4 + 2.56 = 2.96
2.56 + 3.2x + x2 = 2.96

Factor a perfect square on the left side:
(x + 1.6)(x + 1.6) = 2.96

Calculate the square root of the right side: 1.720465053

Break this problem into two subproblems by setting 
(x + 1.6) equal to 1.720465053 and -1.720465053.

Subproblem 1
x + 1.6 = 1.720465053

Simplifying
x + 1.6 = 1.720465053

Reorder the terms:
1.6 + x = 1.720465053

Solving
1.6 + x = 1.720465053

Solving for variable 'x'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + x = 1.720465053 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + x = 1.720465053 + -1.6
x = 1.720465053 + -1.6

Combine like terms: 1.720465053 + -1.6 = 0.120465053
x = 0.120465053

Simplifying
x = 0.120465053

Subproblem 2
x + 1.6 = -1.720465053

Simplifying
x + 1.6 = -1.720465053

Reorder the terms:
1.6 + x = -1.720465053

Solving
1.6 + x = -1.720465053

Solving for variable 'x'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + x = -1.720465053 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + x = -1.720465053 + -1.6
x = -1.720465053 + -1.6

Combine like terms: -1.720465053 + -1.6 = -3.320465053
x = -3.320465053

Simplifying
x = -3.320465053

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.120465053, -3.320465053}