1-4(x-1)=(x-2)(x+2)

Solution for 1-4(x-1)=(x-2)(x+2) equation:

Simplifying
1 + -4(x + -1) = (x + -2)(x + 2)

Reorder the terms:
1 + -4(-1 + x) = (x + -2)(x + 2)
1 + (-1 * -4 + x * -4) = (x + -2)(x + 2)
1 + (4 + -4x) = (x + -2)(x + 2)

Combine like terms: 1 + 4 = 5
5 + -4x = (x + -2)(x + 2)

Reorder the terms:
5 + -4x = (-2 + x)(x + 2)

Reorder the terms:
5 + -4x = (-2 + x)(2 + x)

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

Combine like terms: -2x + 2x = 0
5 + -4x = (-4 + 0 + x2)
5 + -4x = (-4 + x2)

Solving
5 + -4x = -4 + x2

Solving for variable 'x'.

Reorder the terms:
5 + 4 + -4x + -1x2 = -4 + x2 + 4 + -1x2

Combine like terms: 5 + 4 = 9
9 + -4x + -1x2 = -4 + x2 + 4 + -1x2

Reorder the terms:
9 + -4x + -1x2 = -4 + 4 + x2 + -1x2

Combine like terms: -4 + 4 = 0
9 + -4x + -1x2 = 0 + x2 + -1x2
9 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
9 + -4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-9 + 4x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 4x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 4x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 4x + x2 = 0 + 9
4x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
4x + x2 = 9

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 + 4

Reorder the terms:
4 + 4x + x2 = 9 + 4

Combine like terms: 9 + 4 = 13
4 + 4x + x2 = 13

Factor a perfect square on the left side:
(x + 2)(x + 2) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + 2) equal to 3.605551275 and -3.605551275.

Subproblem 1
x + 2 = 3.605551275

Simplifying
x + 2 = 3.605551275

Reorder the terms:
2 + x = 3.605551275

Solving
2 + x = 3.605551275

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 3.605551275 + -2

Combine like terms: 2 + -2 = 0
0 + x = 3.605551275 + -2
x = 3.605551275 + -2

Combine like terms: 3.605551275 + -2 = 1.605551275
x = 1.605551275

Simplifying
x = 1.605551275

Subproblem 2
x + 2 = -3.605551275

Simplifying
x + 2 = -3.605551275

Reorder the terms:
2 + x = -3.605551275

Solving
2 + x = -3.605551275

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -3.605551275 + -2

Combine like terms: 2 + -2 = 0
0 + x = -3.605551275 + -2
x = -3.605551275 + -2

Combine like terms: -3.605551275 + -2 = -5.605551275
x = -5.605551275

Simplifying
x = -5.605551275

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.605551275, -5.605551275}