10x(x+3)-(-9x-4)=x-5+3

Solution for 10x(x+3)-(-9x-4)=x-5+3 equation:

Simplifying
10x(x + 3) + -1(-9x + -4) = x + -5 + 3

Reorder the terms:
10x(3 + x) + -1(-9x + -4) = x + -5 + 3
(3 * 10x + x * 10x) + -1(-9x + -4) = x + -5 + 3
(30x + 10x2) + -1(-9x + -4) = x + -5 + 3

Reorder the terms:
30x + 10x2 + -1(-4 + -9x) = x + -5 + 3
30x + 10x2 + (-4 * -1 + -9x * -1) = x + -5 + 3
30x + 10x2 + (4 + 9x) = x + -5 + 3

Reorder the terms:
4 + 30x + 9x + 10x2 = x + -5 + 3

Combine like terms: 30x + 9x = 39x
4 + 39x + 10x2 = x + -5 + 3

Reorder the terms:
4 + 39x + 10x2 = -5 + 3 + x

Combine like terms: -5 + 3 = -2
4 + 39x + 10x2 = -2 + x

Solving
4 + 39x + 10x2 = -2 + x

Solving for variable 'x'.

Reorder the terms:
4 + 2 + 39x + -1x + 10x2 = -2 + x + 2 + -1x

Combine like terms: 4 + 2 = 6
6 + 39x + -1x + 10x2 = -2 + x + 2 + -1x

Combine like terms: 39x + -1x = 38x
6 + 38x + 10x2 = -2 + x + 2 + -1x

Reorder the terms:
6 + 38x + 10x2 = -2 + 2 + x + -1x

Combine like terms: -2 + 2 = 0
6 + 38x + 10x2 = 0 + x + -1x
6 + 38x + 10x2 = x + -1x

Combine like terms: x + -1x = 0
6 + 38x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 19x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 19x + 5x2)' equal to zero and attempt to solve:

Simplifying
3 + 19x + 5x2 = 0

Solving
3 + 19x + 5x2 = 0

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

Divide each side by '5'.
0.6 + 3.8x + x2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + 3.8x + -0.6 + x2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + 3.8x + x2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + 3.8x + x2 = 0 + -0.6
3.8x + x2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
3.8x + x2 = -0.6

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 = -0.6 + 3.61

Reorder the terms:
3.61 + 3.8x + x2 = -0.6 + 3.61

Combine like terms: -0.6 + 3.61 = 3.01
3.61 + 3.8x + x2 = 3.01

Factor a perfect square on the left side:
(x + 1.9)(x + 1.9) = 3.01

Calculate the square root of the right side: 1.734935157

Break this problem into two subproblems by setting 
(x + 1.9) equal to 1.734935157 and -1.734935157.

Subproblem 1
x + 1.9 = 1.734935157

Simplifying
x + 1.9 = 1.734935157

Reorder the terms:
1.9 + x = 1.734935157

Solving
1.9 + x = 1.734935157

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 = 1.734935157 + -1.9

Combine like terms: 1.9 + -1.9 = 0.0
0.0 + x = 1.734935157 + -1.9
x = 1.734935157 + -1.9

Combine like terms: 1.734935157 + -1.9 = -0.165064843
x = -0.165064843

Simplifying
x = -0.165064843

Subproblem 2
x + 1.9 = -1.734935157

Simplifying
x + 1.9 = -1.734935157

Reorder the terms:
1.9 + x = -1.734935157

Solving
1.9 + x = -1.734935157

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 = -1.734935157 + -1.9

Combine like terms: 1.9 + -1.9 = 0.0
0.0 + x = -1.734935157 + -1.9
x = -1.734935157 + -1.9

Combine like terms: -1.734935157 + -1.9 = -3.634935157
x = -3.634935157

Simplifying
x = -3.634935157

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.165064843, -3.634935157}
Solution
x = {-0.165064843, -3.634935157}