15x(7x+6)=11-(x-10)

Solution for 15x(7x+6)=11-(x-10) equation:

Simplifying
15x(7x + 6) = 11 + -1(x + -10)

Reorder the terms:
15x(6 + 7x) = 11 + -1(x + -10)
(6 * 15x + 7x * 15x) = 11 + -1(x + -10)
(90x + 105x2) = 11 + -1(x + -10)

Reorder the terms:
90x + 105x2 = 11 + -1(-10 + x)
90x + 105x2 = 11 + (-10 * -1 + x * -1)
90x + 105x2 = 11 + (10 + -1x)

Combine like terms: 11 + 10 = 21
90x + 105x2 = 21 + -1x

Solving
90x + 105x2 = 21 + -1x

Solving for variable 'x'.

Reorder the terms:
-21 + 90x + x + 105x2 = 21 + -1x + -21 + x

Combine like terms: 90x + x = 91x
-21 + 91x + 105x2 = 21 + -1x + -21 + x

Reorder the terms:
-21 + 91x + 105x2 = 21 + -21 + -1x + x

Combine like terms: 21 + -21 = 0
-21 + 91x + 105x2 = 0 + -1x + x
-21 + 91x + 105x2 = -1x + x

Combine like terms: -1x + x = 0
-21 + 91x + 105x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-3 + 13x + 15x2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-3 + 13x + 15x2)' equal to zero and attempt to solve:

Simplifying
-3 + 13x + 15x2 = 0

Solving
-3 + 13x + 15x2 = 0

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

Divide each side by '15'.
-0.2 + 0.8666666667x + x2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 0.8666666667x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 0.8666666667x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 0.8666666667x + x2 = 0 + 0.2
0.8666666667x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
0.8666666667x + x2 = 0.2

The x term is 0.8666666667x.  Take half its coefficient (0.4333333334).
Square it (0.1877777778) and add it to both sides.

Add '0.1877777778' to each side of the equation.
0.8666666667x + 0.1877777778 + x2 = 0.2 + 0.1877777778

Reorder the terms:
0.1877777778 + 0.8666666667x + x2 = 0.2 + 0.1877777778

Combine like terms: 0.2 + 0.1877777778 = 0.3877777778
0.1877777778 + 0.8666666667x + x2 = 0.3877777778

Factor a perfect square on the left side:
(x + 0.4333333334)(x + 0.4333333334) = 0.3877777778

Calculate the square root of the right side: 0.622718056

Break this problem into two subproblems by setting 
(x + 0.4333333334) equal to 0.622718056 and -0.622718056.

Subproblem 1
x + 0.4333333334 = 0.622718056

Simplifying
x + 0.4333333334 = 0.622718056

Reorder the terms:
0.4333333334 + x = 0.622718056

Solving
0.4333333334 + x = 0.622718056

Solving for variable 'x'.

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

Add '-0.4333333334' to each side of the equation.
0.4333333334 + -0.4333333334 + x = 0.622718056 + -0.4333333334

Combine like terms: 0.4333333334 + -0.4333333334 = 0.0000000000
0.0000000000 + x = 0.622718056 + -0.4333333334
x = 0.622718056 + -0.4333333334

Combine like terms: 0.622718056 + -0.4333333334 = 0.1893847226
x = 0.1893847226

Simplifying
x = 0.1893847226

Subproblem 2
x + 0.4333333334 = -0.622718056

Simplifying
x + 0.4333333334 = -0.622718056

Reorder the terms:
0.4333333334 + x = -0.622718056

Solving
0.4333333334 + x = -0.622718056

Solving for variable 'x'.

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

Add '-0.4333333334' to each side of the equation.
0.4333333334 + -0.4333333334 + x = -0.622718056 + -0.4333333334

Combine like terms: 0.4333333334 + -0.4333333334 = 0.0000000000
0.0000000000 + x = -0.622718056 + -0.4333333334
x = -0.622718056 + -0.4333333334

Combine like terms: -0.622718056 + -0.4333333334 = -1.0560513894
x = -1.0560513894

Simplifying
x = -1.0560513894

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1893847226, -1.0560513894}
Solution
x = {0.1893847226, -1.0560513894}