16t^2+32t=128

Solution for 16t^2+32t=128 equation:

Simplifying
16t2 + 32t = 128

Reorder the terms:
32t + 16t2 = 128

Solving
32t + 16t2 = 128

Solving for variable 't'.

Reorder the terms:
-128 + 32t + 16t2 = 128 + -128

Combine like terms: 128 + -128 = 0
-128 + 32t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-8 + 2t + t2) = 0

Factor a trinomial.
16((-4 + -1t)(2 + -1t)) = 0

Ignore the factor 16.
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 '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-4, 2}