16x^2-6x=4

Solution for 16x^2-6x=4 equation:

Simplifying
16x2 + -6x = 4

Reorder the terms:
-6x + 16x2 = 4

Solving
-6x + 16x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + -6x + 16x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + -6x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -3x + 8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -3x + 8x2)' equal to zero and attempt to solve:

Simplifying
-2 + -3x + 8x2 = 0

Solving
-2 + -3x + 8x2 = 0

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

Divide each side by '8'.
-0.25 + -0.375x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -0.375x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -0.375x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -0.375x + x2 = 0 + 0.25
-0.375x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-0.375x + x2 = 0.25

The x term is -0.375x.  Take half its coefficient (-0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
-0.375x + 0.03515625 + x2 = 0.25 + 0.03515625

Reorder the terms:
0.03515625 + -0.375x + x2 = 0.25 + 0.03515625

Combine like terms: 0.25 + 0.03515625 = 0.28515625
0.03515625 + -0.375x + x2 = 0.28515625

Factor a perfect square on the left side:
(x + -0.1875)(x + -0.1875) = 0.28515625

Calculate the square root of the right side: 0.534000234

Break this problem into two subproblems by setting 
(x + -0.1875) equal to 0.534000234 and -0.534000234.

Subproblem 1
x + -0.1875 = 0.534000234

Simplifying
x + -0.1875 = 0.534000234

Reorder the terms:
-0.1875 + x = 0.534000234

Solving
-0.1875 + x = 0.534000234

Solving for variable 'x'.

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

Add '0.1875' to each side of the equation.
-0.1875 + 0.1875 + x = 0.534000234 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + x = 0.534000234 + 0.1875
x = 0.534000234 + 0.1875

Combine like terms: 0.534000234 + 0.1875 = 0.721500234
x = 0.721500234

Simplifying
x = 0.721500234

Subproblem 2
x + -0.1875 = -0.534000234

Simplifying
x + -0.1875 = -0.534000234

Reorder the terms:
-0.1875 + x = -0.534000234

Solving
-0.1875 + x = -0.534000234

Solving for variable 'x'.

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

Add '0.1875' to each side of the equation.
-0.1875 + 0.1875 + x = -0.534000234 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + x = -0.534000234 + 0.1875
x = -0.534000234 + 0.1875

Combine like terms: -0.534000234 + 0.1875 = -0.346500234
x = -0.346500234

Simplifying
x = -0.346500234

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.721500234, -0.346500234}
Solution
x = {0.721500234, -0.346500234}