-4(2t-3)(2t-1)=0

Solution for -4(2t-3)(2t-1)=0 equation:

Simplifying
-4(2t + -3)(2t + -1) = 0

Reorder the terms:
-4(-3 + 2t)(2t + -1) = 0

Reorder the terms:
-4(-3 + 2t)(-1 + 2t) = 0

Multiply (-3 + 2t) * (-1 + 2t)
-4(-3(-1 + 2t) + 2t * (-1 + 2t)) = 0
-4((-1 * -3 + 2t * -3) + 2t * (-1 + 2t)) = 0
-4((3 + -6t) + 2t * (-1 + 2t)) = 0
-4(3 + -6t + (-1 * 2t + 2t * 2t)) = 0
-4(3 + -6t + (-2t + 4t2)) = 0

Combine like terms: -6t + -2t = -8t
-4(3 + -8t + 4t2) = 0
(3 * -4 + -8t * -4 + 4t2 * -4) = 0
(-12 + 32t + -16t2) = 0

Solving
-12 + 32t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + 8t + -4t2) = 0

Factor a trinomial.
4((-3 + 2t)(1 + -2t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + 2t)' equal to zero and attempt to solve:

Simplifying
-3 + 2t = 0

Solving
-3 + 2t = 0

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

Add '3' to each side of the equation.
-3 + 3 + 2t = 0 + 3

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

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

Divide each side by '2'.
t = 1.5

Simplifying
t = 1.5
Subproblem 2
Set the factor '(1 + -2t)' equal to zero and attempt to solve:

Simplifying
1 + -2t = 0

Solving
1 + -2t = 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 + -2t = 0 + -1

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

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

Divide each side by '-2'.
t = 0.5

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