16t^2+64t=80

Solution for 16t^2+64t=80 equation:

Simplifying
16t2 + 64t = 80

Reorder the terms:
64t + 16t2 = 80

Solving
64t + 16t2 = 80

Solving for variable 't'.

Reorder the terms:
-80 + 64t + 16t2 = 80 + -80

Combine like terms: 80 + -80 = 0
-80 + 64t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-5 + 4t + t2) = 0

Factor a trinomial.
16((-5 + -1t)(1 + -1t)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-5 + -1t)' equal to zero and attempt to solve:

Simplifying
-5 + -1t = 0

Solving
-5 + -1t = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1t = 0 + 5
-1t = 0 + 5

Combine like terms: 0 + 5 = 5
-1t = 5

Divide each side by '-1'.
t = -5

Simplifying
t = -5
Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

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

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

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

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

Simplifying
t = 1
Solution
t = {-5, 1}