16t^2-16t=32

Solution for 16t^2-16t=32 equation:

Simplifying
16t2 + -16t = 32

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

Solving
-16t + 16t2 = 32

Solving for variable 't'.

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

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

Factor out the Greatest Common Factor (GCF), '16'.
16(-2 + -1t + t2) = 0

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

Ignore the factor 16.
Subproblem 1
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
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 = {-1, 2}