4(t-2)(-4t+1)=0

Solution for 4(t-2)(-4t+1)=0 equation:

Simplifying
4(t + -2)(-4t + 1) = 0

Reorder the terms:
4(-2 + t)(-4t + 1) = 0

Reorder the terms:
4(-2 + t)(1 + -4t) = 0

Multiply (-2 + t) * (1 + -4t)
4(-2(1 + -4t) + t(1 + -4t)) = 0
4((1 * -2 + -4t * -2) + t(1 + -4t)) = 0
4((-2 + 8t) + t(1 + -4t)) = 0
4(-2 + 8t + (1 * t + -4t * t)) = 0
4(-2 + 8t + (1t + -4t2)) = 0

Combine like terms: 8t + 1t = 9t
4(-2 + 9t + -4t2) = 0
(-2 * 4 + 9t * 4 + -4t2 * 4) = 0
(-8 + 36t + -16t2) = 0

Solving
-8 + 36t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + 9t + -4t2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(-2 + t)' equal to zero and attempt to solve:

Simplifying
-2 + t = 0

Solving
-2 + t = 0

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

Add '2' to each side of the equation.
-2 + 2 + t = 0 + 2

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

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

Simplifying
t = 2
Subproblem 2
Set the factor '(1 + -4t)' equal to zero and attempt to solve:

Simplifying
1 + -4t = 0

Solving
1 + -4t = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4t = 0 + -1
-4t = 0 + -1

Combine like terms: 0 + -1 = -1
-4t = -1

Divide each side by '-4'.
t = 0.25

Simplifying
t = 0.25
Solution
t = {2, 0.25}