6x+15x-10x(x+4)=3

Solution for 6x+15x-10x(x+4)=3 equation:

Simplifying
6x + 15x + -10x(x + 4) = 3

Reorder the terms:
6x + 15x + -10x(4 + x) = 3
6x + 15x + (4 * -10x + x * -10x) = 3
6x + 15x + (-40x + -10x2) = 3

Combine like terms: 6x + 15x = 21x
21x + -40x + -10x2 = 3

Combine like terms: 21x + -40x = -19x
-19x + -10x2 = 3

Solving
-19x + -10x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + -19x + -10x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -19x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 19x + 10x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + 19x + 10x2)' equal to zero and attempt to solve:

Simplifying
3 + 19x + 10x2 = 0

Solving
3 + 19x + 10x2 = 0

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

Divide each side by '10'.
0.3 + 1.9x + x2 = 0.0

Move the constant term to the right:

Add '-0.3' to each side of the equation.
0.3 + 1.9x + -0.3 + x2 = 0.0 + -0.3

Reorder the terms:
0.3 + -0.3 + 1.9x + x2 = 0.0 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + 1.9x + x2 = 0.0 + -0.3
1.9x + x2 = 0.0 + -0.3

Combine like terms: 0.0 + -0.3 = -0.3
1.9x + x2 = -0.3

The x term is 1.9x.  Take half its coefficient (0.95).
Square it (0.9025) and add it to both sides.

Add '0.9025' to each side of the equation.
1.9x + 0.9025 + x2 = -0.3 + 0.9025

Reorder the terms:
0.9025 + 1.9x + x2 = -0.3 + 0.9025

Combine like terms: -0.3 + 0.9025 = 0.6025
0.9025 + 1.9x + x2 = 0.6025

Factor a perfect square on the left side:
(x + 0.95)(x + 0.95) = 0.6025

Calculate the square root of the right side: 0.776208735

Break this problem into two subproblems by setting 
(x + 0.95) equal to 0.776208735 and -0.776208735.

Subproblem 1
x + 0.95 = 0.776208735

Simplifying
x + 0.95 = 0.776208735

Reorder the terms:
0.95 + x = 0.776208735

Solving
0.95 + x = 0.776208735

Solving for variable 'x'.

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

Add '-0.95' to each side of the equation.
0.95 + -0.95 + x = 0.776208735 + -0.95

Combine like terms: 0.95 + -0.95 = 0.00
0.00 + x = 0.776208735 + -0.95
x = 0.776208735 + -0.95

Combine like terms: 0.776208735 + -0.95 = -0.173791265
x = -0.173791265

Simplifying
x = -0.173791265

Subproblem 2
x + 0.95 = -0.776208735

Simplifying
x + 0.95 = -0.776208735

Reorder the terms:
0.95 + x = -0.776208735

Solving
0.95 + x = -0.776208735

Solving for variable 'x'.

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

Add '-0.95' to each side of the equation.
0.95 + -0.95 + x = -0.776208735 + -0.95

Combine like terms: 0.95 + -0.95 = 0.00
0.00 + x = -0.776208735 + -0.95
x = -0.776208735 + -0.95

Combine like terms: -0.776208735 + -0.95 = -1.726208735
x = -1.726208735

Simplifying
x = -1.726208735

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.173791265, -1.726208735}
Solution
x = {-0.173791265, -1.726208735}