4-[4(2k-3)(k-1)]=0

Solution for 4-[4(2k-3)(k-1)]=0 equation:

Simplifying
4 + -1[4(2k + -3)(k + -1)] = 0

Reorder the terms:
4 + -1[4(-3 + 2k)(k + -1)] = 0

Reorder the terms:
4 + -1[4(-3 + 2k)(-1 + k)] = 0

Multiply (-3 + 2k) * (-1 + k)
4 + -1[4(-3(-1 + k) + 2k * (-1 + k))] = 0
4 + -1[4((-1 * -3 + k * -3) + 2k * (-1 + k))] = 0
4 + -1[4((3 + -3k) + 2k * (-1 + k))] = 0
4 + -1[4(3 + -3k + (-1 * 2k + k * 2k))] = 0
4 + -1[4(3 + -3k + (-2k + 2k2))] = 0

Combine like terms: -3k + -2k = -5k
4 + -1[4(3 + -5k + 2k2)] = 0
4 + -1[(3 * 4 + -5k * 4 + 2k2 * 4)] = 0
4 + -1[(12 + -20k + 8k2)] = 0
4 + [12 * -1 + -20k * -1 + 8k2 * -1] = 0
4 + [-12 + 20k + -8k2] = 0

Combine like terms: 4 + -12 = -8
-8 + 20k + -8k2 = 0

Solving
-8 + 20k + -8k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + 5k + -2k2) = 0

Factor a trinomial.
4((-2 + k)(1 + -2k)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-2 + k)' equal to zero and attempt to solve:

Simplifying
-2 + k = 0

Solving
-2 + k = 0

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

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

Combine like terms: -2 + 2 = 0
0 + k = 0 + 2
k = 0 + 2

Combine like terms: 0 + 2 = 2
k = 2

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

Simplifying
1 + -2k = 0

Solving
1 + -2k = 0

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

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

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

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

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

Simplifying
k = 0.5
Solution
k = {2, 0.5}