4t^2-56t+160=0

Solution for 4t^2-56t+160=0 equation:

Simplifying
4t2 + -56t + 160 = 0

Reorder the terms:
160 + -56t + 4t2 = 0

Solving
160 + -56t + 4t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(40 + -14t + t2) = 0

Factor a trinomial.
4((4 + -1t)(10 + -1t)) = 0

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

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

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

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

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

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Subproblem 2
Set the factor '(10 + -1t)' equal to zero and attempt to solve:

Simplifying
10 + -1t = 0

Solving
10 + -1t = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1t = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1t = 0 + -10
-1t = 0 + -10

Combine like terms: 0 + -10 = -10
-1t = -10

Divide each side by '-1'.
t = 10

Simplifying
t = 10
Solution
t = {4, 10}