1=4(x-1)(x-1)

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

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

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

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

Multiply (-1 + x) * (-1 + x)
1 = 4(-1(-1 + x) + x(-1 + x))
1 = 4((-1 * -1 + x * -1) + x(-1 + x))
1 = 4((1 + -1x) + x(-1 + x))
1 = 4(1 + -1x + (-1 * x + x * x))
1 = 4(1 + -1x + (-1x + x2))

Combine like terms: -1x + -1x = -2x
1 = 4(1 + -2x + x2)
1 = (1 * 4 + -2x * 4 + x2 * 4)
1 = (4 + -8x + 4x2)

Solving
1 = 4 + -8x + 4x2

Solving for variable 'x'.

Combine like terms: 1 + -4 = -3
-3 + 8x + -4x2 = 4 + -8x + 4x2 + -4 + 8x + -4x2

Reorder the terms:
-3 + 8x + -4x2 = 4 + -4 + -8x + 8x + 4x2 + -4x2

Combine like terms: 4 + -4 = 0
-3 + 8x + -4x2 = 0 + -8x + 8x + 4x2 + -4x2
-3 + 8x + -4x2 = -8x + 8x + 4x2 + -4x2

Combine like terms: -8x + 8x = 0
-3 + 8x + -4x2 = 0 + 4x2 + -4x2
-3 + 8x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-3 + 8x + -4x2 = 0

Factor a trinomial.
(-3 + 2x)(1 + -2x) = 0

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

Simplifying
-3 + 2x = 0

Solving
-3 + 2x = 0

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

Add '3' to each side of the equation.
-3 + 3 + 2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2x = 0 + 3
2x = 0 + 3

Combine like terms: 0 + 3 = 3
2x = 3

Divide each side by '2'.
x = 1.5

Simplifying
x = 1.5
Subproblem 2
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {1.5, 0.5}