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

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

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

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

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

Reorder the terms:
-1 + -6x + -3x2 = 2(-5 + x) + -5x
-1 + -6x + -3x2 = (-5 * 2 + x * 2) + -5x
-1 + -6x + -3x2 = (-10 + 2x) + -5x

Combine like terms: 2x + -5x = -3x
-1 + -6x + -3x2 = -10 + -3x

Solving
-1 + -6x + -3x2 = -10 + -3x

Solving for variable 'x'.

Reorder the terms:
-1 + 10 + -6x + 3x + -3x2 = -10 + -3x + 10 + 3x

Combine like terms: -1 + 10 = 9
9 + -6x + 3x + -3x2 = -10 + -3x + 10 + 3x

Combine like terms: -6x + 3x = -3x
9 + -3x + -3x2 = -10 + -3x + 10 + 3x

Reorder the terms:
9 + -3x + -3x2 = -10 + 10 + -3x + 3x

Combine like terms: -10 + 10 = 0
9 + -3x + -3x2 = 0 + -3x + 3x
9 + -3x + -3x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
9 + -3x + -3x2 = 0

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

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

Simplifying
3 + -1x + -1x2 = 0

Solving
3 + -1x + -1x2 = 0

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

Divide each side by '-1'.
-3 + x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + x + x2 = 0 + 3

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

Combine like terms: 0 + 3 = 3
x + x2 = 3

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 3 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 3 + 0.25

Combine like terms: 3 + 0.25 = 3.25
1.25 + x2 = 3.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.802775638 and -1.802775638.

Subproblem 1
x + 0.5 = 1.802775638

Simplifying
x + 0.5 = 1.802775638

Reorder the terms:
0.5 + x = 1.802775638

Solving
0.5 + x = 1.802775638

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.802775638 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.802775638 + -0.5
x = 1.802775638 + -0.5

Combine like terms: 1.802775638 + -0.5 = 1.302775638
x = 1.302775638

Simplifying
x = 1.302775638

Subproblem 2
x + 0.5 = -1.802775638

Simplifying
x + 0.5 = -1.802775638

Reorder the terms:
0.5 + x = -1.802775638

Solving
0.5 + x = -1.802775638

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.802775638 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.802775638 + -0.5
x = -1.802775638 + -0.5

Combine like terms: -1.802775638 + -0.5 = -2.302775638
x = -2.302775638

Simplifying
x = -2.302775638

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.302775638, -2.302775638}
Solution
x = {1.302775638, -2.302775638}