0=x(-5x-10)-(7x+3)

Solution for 0=x(-5x-10)-(7x+3) equation:

Simplifying
0 = x(-5x + -10) + -1(7x + 3)

Reorder the terms:
0 = x(-10 + -5x) + -1(7x + 3)
0 = (-10 * x + -5x * x) + -1(7x + 3)
0 = (-10x + -5x2) + -1(7x + 3)

Reorder the terms:
0 = -10x + -5x2 + -1(3 + 7x)
0 = -10x + -5x2 + (3 * -1 + 7x * -1)
0 = -10x + -5x2 + (-3 + -7x)

Reorder the terms:
0 = -3 + -10x + -7x + -5x2

Combine like terms: -10x + -7x = -17x
0 = -3 + -17x + -5x2

Solving
0 = -3 + -17x + -5x2

Solving for variable 'x'.

Combine like terms: 0 + 3 = 3
3 + 17x + 5x2 = -3 + -17x + -5x2 + 3 + 17x + 5x2

Reorder the terms:
3 + 17x + 5x2 = -3 + 3 + -17x + 17x + -5x2 + 5x2

Combine like terms: -3 + 3 = 0
3 + 17x + 5x2 = 0 + -17x + 17x + -5x2 + 5x2
3 + 17x + 5x2 = -17x + 17x + -5x2 + 5x2

Combine like terms: -17x + 17x = 0
3 + 17x + 5x2 = 0 + -5x2 + 5x2
3 + 17x + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
3 + 17x + 5x2 = 0

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

Divide each side by '5'.
0.6 + 3.4x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + 3.4x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + 3.4x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + 3.4x + x2 = 0 + -0.6
3.4x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
3.4x + x2 = -0.6

The x term is 3.4x.  Take half its coefficient (1.7).
Square it (2.89) and add it to both sides.

Add '2.89' to each side of the equation.
3.4x + 2.89 + x2 = -0.6 + 2.89

Reorder the terms:
2.89 + 3.4x + x2 = -0.6 + 2.89

Combine like terms: -0.6 + 2.89 = 2.29
2.89 + 3.4x + x2 = 2.29

Factor a perfect square on the left side:
(x + 1.7)(x + 1.7) = 2.29

Calculate the square root of the right side: 1.513274595

Break this problem into two subproblems by setting 
(x + 1.7) equal to 1.513274595 and -1.513274595.

Subproblem 1
x + 1.7 = 1.513274595

Simplifying
x + 1.7 = 1.513274595

Reorder the terms:
1.7 + x = 1.513274595

Solving
1.7 + x = 1.513274595

Solving for variable 'x'.

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

Add '-1.7' to each side of the equation.
1.7 + -1.7 + x = 1.513274595 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + x = 1.513274595 + -1.7
x = 1.513274595 + -1.7

Combine like terms: 1.513274595 + -1.7 = -0.186725405
x = -0.186725405

Simplifying
x = -0.186725405

Subproblem 2
x + 1.7 = -1.513274595

Simplifying
x + 1.7 = -1.513274595

Reorder the terms:
1.7 + x = -1.513274595

Solving
1.7 + x = -1.513274595

Solving for variable 'x'.

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

Add '-1.7' to each side of the equation.
1.7 + -1.7 + x = -1.513274595 + -1.7

Combine like terms: 1.7 + -1.7 = 0.0
0.0 + x = -1.513274595 + -1.7
x = -1.513274595 + -1.7

Combine like terms: -1.513274595 + -1.7 = -3.213274595
x = -3.213274595

Simplifying
x = -3.213274595

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.186725405, -3.213274595}