(.5)32t^2+16t=320

Solution for (.5)32t^2+16t=320 equation:

Simplifying
(0.5) * 32t2 + 16t = 320

Multiply 0.5 * 32
16t2 + 16t = 320

Reorder the terms:
16t + 16t2 = 320

Solving
16t + 16t2 = 320

Solving for variable 't'.

Reorder the terms:
-320 + 16t + 16t2 = 320 + -320

Combine like terms: 320 + -320 = 0
-320 + 16t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-20 + t + t2) = 0

Factor a trinomial.
16((-5 + -1t)(4 + -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 '(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
Solution
t = {-5, 4}