20t-8t^2+12=0

Solution for 20t-8t^2+12=0 equation:

Simplifying
20t + -8t2 + 12 = 0

Reorder the terms:
12 + 20t + -8t2 = 0

Solving
12 + 20t + -8t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 5t + -2t2) = 0

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

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

Simplifying
3 + -1t = 0

Solving
3 + -1t = 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 + -1t = 0 + -3

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

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

Divide each side by '-1'.
t = 3

Simplifying
t = 3
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 = {3, -0.5}