16x-3(4x+7)=6x(2x+21)

Solution for 16x-3(4x+7)=6x(2x+21) equation:

Simplifying
16x + -3(4x + 7) = 6x(2x + 21)

Reorder the terms:
16x + -3(7 + 4x) = 6x(2x + 21)
16x + (7 * -3 + 4x * -3) = 6x(2x + 21)
16x + (-21 + -12x) = 6x(2x + 21)

Reorder the terms:
-21 + 16x + -12x = 6x(2x + 21)

Combine like terms: 16x + -12x = 4x
-21 + 4x = 6x(2x + 21)

Reorder the terms:
-21 + 4x = 6x(21 + 2x)
-21 + 4x = (21 * 6x + 2x * 6x)
-21 + 4x = (126x + 12x2)

Solving
-21 + 4x = 126x + 12x2

Solving for variable 'x'.

Combine like terms: 4x + -126x = -122x
-21 + -122x + -12x2 = 126x + 12x2 + -126x + -12x2

Reorder the terms:
-21 + -122x + -12x2 = 126x + -126x + 12x2 + -12x2

Combine like terms: 126x + -126x = 0
-21 + -122x + -12x2 = 0 + 12x2 + -12x2
-21 + -122x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-21 + -122x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(21 + 122x + 12x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(21 + 122x + 12x2)' equal to zero and attempt to solve:

Simplifying
21 + 122x + 12x2 = 0

Solving
21 + 122x + 12x2 = 0

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

Divide each side by '12'.
1.75 + 10.16666667x + x2 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + 10.16666667x + -1.75 + x2 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + 10.16666667x + x2 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + 10.16666667x + x2 = 0 + -1.75
10.16666667x + x2 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
10.16666667x + x2 = -1.75

The x term is 10.16666667x.  Take half its coefficient (5.083333335).
Square it (25.84027779) and add it to both sides.

Add '25.84027779' to each side of the equation.
10.16666667x + 25.84027779 + x2 = -1.75 + 25.84027779

Reorder the terms:
25.84027779 + 10.16666667x + x2 = -1.75 + 25.84027779

Combine like terms: -1.75 + 25.84027779 = 24.09027779
25.84027779 + 10.16666667x + x2 = 24.09027779

Factor a perfect square on the left side:
(x + 5.083333335)(x + 5.083333335) = 24.09027779

Calculate the square root of the right side: 4.908184775

Break this problem into two subproblems by setting 
(x + 5.083333335) equal to 4.908184775 and -4.908184775.

Subproblem 1
x + 5.083333335 = 4.908184775

Simplifying
x + 5.083333335 = 4.908184775

Reorder the terms:
5.083333335 + x = 4.908184775

Solving
5.083333335 + x = 4.908184775

Solving for variable 'x'.

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

Add '-5.083333335' to each side of the equation.
5.083333335 + -5.083333335 + x = 4.908184775 + -5.083333335

Combine like terms: 5.083333335 + -5.083333335 = 0.000000000
0.000000000 + x = 4.908184775 + -5.083333335
x = 4.908184775 + -5.083333335

Combine like terms: 4.908184775 + -5.083333335 = -0.17514856
x = -0.17514856

Simplifying
x = -0.17514856

Subproblem 2
x + 5.083333335 = -4.908184775

Simplifying
x + 5.083333335 = -4.908184775

Reorder the terms:
5.083333335 + x = -4.908184775

Solving
5.083333335 + x = -4.908184775

Solving for variable 'x'.

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

Add '-5.083333335' to each side of the equation.
5.083333335 + -5.083333335 + x = -4.908184775 + -5.083333335

Combine like terms: 5.083333335 + -5.083333335 = 0.000000000
0.000000000 + x = -4.908184775 + -5.083333335
x = -4.908184775 + -5.083333335

Combine like terms: -4.908184775 + -5.083333335 = -9.99151811
x = -9.99151811

Simplifying
x = -9.99151811

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.17514856, -9.99151811}
Solution
x = {-0.17514856, -9.99151811}