4(3x^2-12x+28)=1

Solution for 4(3x^2-12x+28)=1 equation:

Simplifying
4(3x2 + -12x + 28) = 1

Reorder the terms:
4(28 + -12x + 3x2) = 1
(28 * 4 + -12x * 4 + 3x2 * 4) = 1
(112 + -48x + 12x2) = 1

Solving
112 + -48x + 12x2 = 1

Solving for variable 'x'.

Reorder the terms:
112 + -1 + -48x + 12x2 = 1 + -1

Combine like terms: 112 + -1 = 111
111 + -48x + 12x2 = 1 + -1

Combine like terms: 1 + -1 = 0
111 + -48x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(37 + -16x + 4x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(37 + -16x + 4x2)' equal to zero and attempt to solve:

Simplifying
37 + -16x + 4x2 = 0

Solving
37 + -16x + 4x2 = 0

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

Divide each side by '4'.
9.25 + -4x + x2 = 0

Move the constant term to the right:

Add '-9.25' to each side of the equation.
9.25 + -4x + -9.25 + x2 = 0 + -9.25

Reorder the terms:
9.25 + -9.25 + -4x + x2 = 0 + -9.25

Combine like terms: 9.25 + -9.25 = 0.00
0.00 + -4x + x2 = 0 + -9.25
-4x + x2 = 0 + -9.25

Combine like terms: 0 + -9.25 = -9.25
-4x + x2 = -9.25

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -9.25 + 4

Reorder the terms:
4 + -4x + x2 = -9.25 + 4

Combine like terms: -9.25 + 4 = -5.25
4 + -4x + x2 = -5.25

Factor a perfect square on the left side:
(x + -2)(x + -2) = -5.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.