16x(x+2)=142-(4x-11)*6

Solution for 16x(x+2)=142-(4x-11)*6 equation:

Simplifying
16x(x + 2) = 142 + -1(4x + -11) * 6

Reorder the terms:
16x(2 + x) = 142 + -1(4x + -11) * 6
(2 * 16x + x * 16x) = 142 + -1(4x + -11) * 6
(32x + 16x2) = 142 + -1(4x + -11) * 6

Reorder the terms:
32x + 16x2 = 142 + -1(-11 + 4x) * 6

Reorder the terms for easier multiplication:
32x + 16x2 = 142 + -1 * 6(-11 + 4x)

Multiply -1 * 6
32x + 16x2 = 142 + -6(-11 + 4x)
32x + 16x2 = 142 + (-11 * -6 + 4x * -6)
32x + 16x2 = 142 + (66 + -24x)

Combine like terms: 142 + 66 = 208
32x + 16x2 = 208 + -24x

Solving
32x + 16x2 = 208 + -24x

Solving for variable 'x'.

Reorder the terms:
-208 + 32x + 24x + 16x2 = 208 + -24x + -208 + 24x

Combine like terms: 32x + 24x = 56x
-208 + 56x + 16x2 = 208 + -24x + -208 + 24x

Reorder the terms:
-208 + 56x + 16x2 = 208 + -208 + -24x + 24x

Combine like terms: 208 + -208 = 0
-208 + 56x + 16x2 = 0 + -24x + 24x
-208 + 56x + 16x2 = -24x + 24x

Combine like terms: -24x + 24x = 0
-208 + 56x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-26 + 7x + 2x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-26 + 7x + 2x2)' equal to zero and attempt to solve:

Simplifying
-26 + 7x + 2x2 = 0

Solving
-26 + 7x + 2x2 = 0

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

Divide each side by '2'.
-13 + 3.5x + x2 = 0

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + 3.5x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + 3.5x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 3.5x + x2 = 0 + 13
3.5x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
3.5x + x2 = 13

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 13 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 13 + 3.0625

Combine like terms: 13 + 3.0625 = 16.0625
3.0625 + 3.5x + x2 = 16.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 16.0625

Calculate the square root of the right side: 4.007804885

Break this problem into two subproblems by setting 
(x + 1.75) equal to 4.007804885 and -4.007804885.

Subproblem 1
x + 1.75 = 4.007804885

Simplifying
x + 1.75 = 4.007804885

Reorder the terms:
1.75 + x = 4.007804885

Solving
1.75 + x = 4.007804885

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 4.007804885 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 4.007804885 + -1.75
x = 4.007804885 + -1.75

Combine like terms: 4.007804885 + -1.75 = 2.257804885
x = 2.257804885

Simplifying
x = 2.257804885

Subproblem 2
x + 1.75 = -4.007804885

Simplifying
x + 1.75 = -4.007804885

Reorder the terms:
1.75 + x = -4.007804885

Solving
1.75 + x = -4.007804885

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -4.007804885 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -4.007804885 + -1.75
x = -4.007804885 + -1.75

Combine like terms: -4.007804885 + -1.75 = -5.757804885
x = -5.757804885

Simplifying
x = -5.757804885

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.257804885, -5.757804885}
Solution
x = {2.257804885, -5.757804885}