32t^2-60t+18=0

Solution for 32t^2-60t+18=0 equation:

Simplifying
32t2 + -60t + 18 = 0

Reorder the terms:
18 + -60t + 32t2 = 0

Solving
18 + -60t + 32t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -30t + 16t2) = 0

Factor a trinomial.
2((3 + -8t)(3 + -2t)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -8t)' equal to zero and attempt to solve:

Simplifying
3 + -8t = 0

Solving
3 + -8t = 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 + -8t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8t = 0 + -3
-8t = 0 + -3

Combine like terms: 0 + -3 = -3
-8t = -3

Divide each side by '-8'.
t = 0.375

Simplifying
t = 0.375
Subproblem 2
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
Solution
t = {0.375, 1.5}