6x^2+11x-16=x-8

Solution for 6x^2+11x-16=x-8 equation:

Simplifying
6x2 + 11x + -16 = x + -8

Reorder the terms:
-16 + 11x + 6x2 = x + -8

Reorder the terms:
-16 + 11x + 6x2 = -8 + x

Solving
-16 + 11x + 6x2 = -8 + x

Solving for variable 'x'.

Reorder the terms:
-16 + 8 + 11x + -1x + 6x2 = -8 + x + 8 + -1x

Combine like terms: -16 + 8 = -8
-8 + 11x + -1x + 6x2 = -8 + x + 8 + -1x

Combine like terms: 11x + -1x = 10x
-8 + 10x + 6x2 = -8 + x + 8 + -1x

Reorder the terms:
-8 + 10x + 6x2 = -8 + 8 + x + -1x

Combine like terms: -8 + 8 = 0
-8 + 10x + 6x2 = 0 + x + -1x
-8 + 10x + 6x2 = x + -1x

Combine like terms: x + -1x = 0
-8 + 10x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 5x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + 5x + 3x2)' equal to zero and attempt to solve:

Simplifying
-4 + 5x + 3x2 = 0

Solving
-4 + 5x + 3x2 = 0

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

Divide each side by '3'.
-1.333333333 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 1.666666667x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 1.666666667x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 1.666666667x + x2 = 0 + 1.333333333
1.666666667x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
1.666666667x + x2 = 1.333333333

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 1.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 1.333333333 + 0.6944444447

Combine like terms: 1.333333333 + 0.6944444447 = 2.0277777777
0.6944444447 + 1.666666667x + x2 = 2.0277777777

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 2.0277777777

Calculate the square root of the right side: 1.424000624

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 1.424000624 and -1.424000624.

Subproblem 1
x + 0.8333333335 = 1.424000624

Simplifying
x + 0.8333333335 = 1.424000624

Reorder the terms:
0.8333333335 + x = 1.424000624

Solving
0.8333333335 + x = 1.424000624

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 1.424000624 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 1.424000624 + -0.8333333335
x = 1.424000624 + -0.8333333335

Combine like terms: 1.424000624 + -0.8333333335 = 0.5906672905
x = 0.5906672905

Simplifying
x = 0.5906672905

Subproblem 2
x + 0.8333333335 = -1.424000624

Simplifying
x + 0.8333333335 = -1.424000624

Reorder the terms:
0.8333333335 + x = -1.424000624

Solving
0.8333333335 + x = -1.424000624

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -1.424000624 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -1.424000624 + -0.8333333335
x = -1.424000624 + -0.8333333335

Combine like terms: -1.424000624 + -0.8333333335 = -2.2573339575
x = -2.2573339575

Simplifying
x = -2.2573339575

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5906672905, -2.2573339575}
Solution
x = {0.5906672905, -2.2573339575}