-3(2x-1)(2x-1)+5=-1

Solution for -3(2x-1)(2x-1)+5=-1 equation:

Simplifying
-3(2x + -1)(2x + -1) + 5 = -1

Reorder the terms:
-3(-1 + 2x)(2x + -1) + 5 = -1

Reorder the terms:
-3(-1 + 2x)(-1 + 2x) + 5 = -1

Multiply (-1 + 2x) * (-1 + 2x)
-3(-1(-1 + 2x) + 2x * (-1 + 2x)) + 5 = -1
-3((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) + 5 = -1
-3((1 + -2x) + 2x * (-1 + 2x)) + 5 = -1
-3(1 + -2x + (-1 * 2x + 2x * 2x)) + 5 = -1
-3(1 + -2x + (-2x + 4x2)) + 5 = -1

Combine like terms: -2x + -2x = -4x
-3(1 + -4x + 4x2) + 5 = -1
(1 * -3 + -4x * -3 + 4x2 * -3) + 5 = -1
(-3 + 12x + -12x2) + 5 = -1

Reorder the terms:
-3 + 5 + 12x + -12x2 = -1

Combine like terms: -3 + 5 = 2
2 + 12x + -12x2 = -1

Solving
2 + 12x + -12x2 = -1

Solving for variable 'x'.

Reorder the terms:
2 + 1 + 12x + -12x2 = -1 + 1

Combine like terms: 2 + 1 = 3
3 + 12x + -12x2 = -1 + 1

Combine like terms: -1 + 1 = 0
3 + 12x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 4x + -4x2) = 0

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

Simplifying
1 + 4x + -4x2 = 0

Solving
1 + 4x + -4x2 = 0

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

Divide each side by '-4'.
-0.25 + -1x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -1x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -1x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -1x + x2 = 0 + 0.25
-1x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-1x + x2 = 0.25

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 0.25 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 0.25 + 0.25

Combine like terms: 0.25 + 0.25 = 0.5
0.25 + -1x + x2 = 0.5

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.707106781 and -0.707106781.

Subproblem 1
x + -0.5 = 0.707106781

Simplifying
x + -0.5 = 0.707106781

Reorder the terms:
-0.5 + x = 0.707106781

Solving
-0.5 + x = 0.707106781

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 0.707106781 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 0.707106781 + 0.5
x = 0.707106781 + 0.5

Combine like terms: 0.707106781 + 0.5 = 1.207106781
x = 1.207106781

Simplifying
x = 1.207106781

Subproblem 2
x + -0.5 = -0.707106781

Simplifying
x + -0.5 = -0.707106781

Reorder the terms:
-0.5 + x = -0.707106781

Solving
-0.5 + x = -0.707106781

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -0.707106781 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -0.707106781 + 0.5
x = -0.707106781 + 0.5

Combine like terms: -0.707106781 + 0.5 = -0.207106781
x = -0.207106781

Simplifying
x = -0.207106781

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.207106781, -0.207106781}
Solution
x = {1.207106781, -0.207106781}