4(x-1)(x-1)=16

Solution for 4(x-1)(x-1)=16 equation:

Simplifying
4(x + -1)(x + -1) = 16

Reorder the terms:
4(-1 + x)(x + -1) = 16

Reorder the terms:
4(-1 + x)(-1 + x) = 16

Multiply (-1 + x) * (-1 + x)
4(-1(-1 + x) + x(-1 + x)) = 16
4((-1 * -1 + x * -1) + x(-1 + x)) = 16
4((1 + -1x) + x(-1 + x)) = 16
4(1 + -1x + (-1 * x + x * x)) = 16
4(1 + -1x + (-1x + x2)) = 16

Combine like terms: -1x + -1x = -2x
4(1 + -2x + x2) = 16
(1 * 4 + -2x * 4 + x2 * 4) = 16
(4 + -8x + 4x2) = 16

Solving
4 + -8x + 4x2 = 16

Solving for variable 'x'.

Reorder the terms:
4 + -16 + -8x + 4x2 = 16 + -16

Combine like terms: 4 + -16 = -12
-12 + -8x + 4x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-12 + -8x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + -2x + x2) = 0

Factor a trinomial.
4((-1 + -1x)(3 + -1x)) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

Divide each side by '-1'.
x = -1

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-1, 3}