16x^2-42x+6=26

Solution for 16x^2-42x+6=26 equation:

Simplifying
16x2 + -42x + 6 = 26

Reorder the terms:
6 + -42x + 16x2 = 26

Solving
6 + -42x + 16x2 = 26

Solving for variable 'x'.

Reorder the terms:
6 + -26 + -42x + 16x2 = 26 + -26

Combine like terms: 6 + -26 = -20
-20 + -42x + 16x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-20 + -42x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -21x + 8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-10 + -21x + 8x2)' equal to zero and attempt to solve:

Simplifying
-10 + -21x + 8x2 = 0

Solving
-10 + -21x + 8x2 = 0

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

Divide each side by '8'.
-1.25 + -2.625x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -2.625x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -2.625x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -2.625x + x2 = 0 + 1.25
-2.625x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-2.625x + x2 = 1.25

The x term is -2.625x.  Take half its coefficient (-1.3125).
Square it (1.72265625) and add it to both sides.

Add '1.72265625' to each side of the equation.
-2.625x + 1.72265625 + x2 = 1.25 + 1.72265625

Reorder the terms:
1.72265625 + -2.625x + x2 = 1.25 + 1.72265625

Combine like terms: 1.25 + 1.72265625 = 2.97265625
1.72265625 + -2.625x + x2 = 2.97265625

Factor a perfect square on the left side:
(x + -1.3125)(x + -1.3125) = 2.97265625

Calculate the square root of the right side: 1.724139278

Break this problem into two subproblems by setting 
(x + -1.3125) equal to 1.724139278 and -1.724139278.

Subproblem 1
x + -1.3125 = 1.724139278

Simplifying
x + -1.3125 = 1.724139278

Reorder the terms:
-1.3125 + x = 1.724139278

Solving
-1.3125 + x = 1.724139278

Solving for variable 'x'.

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

Add '1.3125' to each side of the equation.
-1.3125 + 1.3125 + x = 1.724139278 + 1.3125

Combine like terms: -1.3125 + 1.3125 = 0.0000
0.0000 + x = 1.724139278 + 1.3125
x = 1.724139278 + 1.3125

Combine like terms: 1.724139278 + 1.3125 = 3.036639278
x = 3.036639278

Simplifying
x = 3.036639278

Subproblem 2
x + -1.3125 = -1.724139278

Simplifying
x + -1.3125 = -1.724139278

Reorder the terms:
-1.3125 + x = -1.724139278

Solving
-1.3125 + x = -1.724139278

Solving for variable 'x'.

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

Add '1.3125' to each side of the equation.
-1.3125 + 1.3125 + x = -1.724139278 + 1.3125

Combine like terms: -1.3125 + 1.3125 = 0.0000
0.0000 + x = -1.724139278 + 1.3125
x = -1.724139278 + 1.3125

Combine like terms: -1.724139278 + 1.3125 = -0.411639278
x = -0.411639278

Simplifying
x = -0.411639278

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.036639278, -0.411639278}
Solution
x = {3.036639278, -0.411639278}