-5x(x+1)+3x+2=6x+4

Solution for -5x(x+1)+3x+2=6x+4 equation:

Simplifying
-5x(x + 1) + 3x + 2 = 6x + 4

Reorder the terms:
-5x(1 + x) + 3x + 2 = 6x + 4
(1 * -5x + x * -5x) + 3x + 2 = 6x + 4
(-5x + -5x2) + 3x + 2 = 6x + 4

Reorder the terms:
2 + -5x + 3x + -5x2 = 6x + 4

Combine like terms: -5x + 3x = -2x
2 + -2x + -5x2 = 6x + 4

Reorder the terms:
2 + -2x + -5x2 = 4 + 6x

Solving
2 + -2x + -5x2 = 4 + 6x

Solving for variable 'x'.

Reorder the terms:
2 + -4 + -2x + -6x + -5x2 = 4 + 6x + -4 + -6x

Combine like terms: 2 + -4 = -2
-2 + -2x + -6x + -5x2 = 4 + 6x + -4 + -6x

Combine like terms: -2x + -6x = -8x
-2 + -8x + -5x2 = 4 + 6x + -4 + -6x

Reorder the terms:
-2 + -8x + -5x2 = 4 + -4 + 6x + -6x

Combine like terms: 4 + -4 = 0
-2 + -8x + -5x2 = 0 + 6x + -6x
-2 + -8x + -5x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-2 + -8x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 8x + 5x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + 8x + 5x2)' equal to zero and attempt to solve:

Simplifying
2 + 8x + 5x2 = 0

Solving
2 + 8x + 5x2 = 0

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

Divide each side by '5'.
0.4 + 1.6x + x2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + 1.6x + -0.4 + x2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + 1.6x + x2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + 1.6x + x2 = 0 + -0.4
1.6x + x2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
1.6x + x2 = -0.4

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 = -0.4 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = -0.4 + 0.64

Combine like terms: -0.4 + 0.64 = 0.24
0.64 + 1.6x + x2 = 0.24

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = 0.24

Calculate the square root of the right side: 0.489897949

Break this problem into two subproblems by setting 
(x + 0.8) equal to 0.489897949 and -0.489897949.

Subproblem 1
x + 0.8 = 0.489897949

Simplifying
x + 0.8 = 0.489897949

Reorder the terms:
0.8 + x = 0.489897949

Solving
0.8 + x = 0.489897949

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 = 0.489897949 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = 0.489897949 + -0.8
x = 0.489897949 + -0.8

Combine like terms: 0.489897949 + -0.8 = -0.310102051
x = -0.310102051

Simplifying
x = -0.310102051

Subproblem 2
x + 0.8 = -0.489897949

Simplifying
x + 0.8 = -0.489897949

Reorder the terms:
0.8 + x = -0.489897949

Solving
0.8 + x = -0.489897949

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 = -0.489897949 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = -0.489897949 + -0.8
x = -0.489897949 + -0.8

Combine like terms: -0.489897949 + -0.8 = -1.289897949
x = -1.289897949

Simplifying
x = -1.289897949

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.310102051, -1.289897949}
Solution
x = {-0.310102051, -1.289897949}