16(-T^2+2T+3)=0

Solution for 16(-T^2+2T+3)=0 equation:

Simplifying
16(-1T2 + 2T + 3) = 0

Reorder the terms:
16(3 + 2T + -1T2) = 0
(3 * 16 + 2T * 16 + -1T2 * 16) = 0
(48 + 32T + -16T2) = 0

Solving
48 + 32T + -16T2 = 0

Solving for variable 'T'.

Factor out the Greatest Common Factor (GCF), '16'.
16(3 + 2T + -1T2) = 0

Factor a trinomial.
16((3 + -1T)(1 + T)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(3 + -1T)' equal to zero and attempt to solve:

Simplifying
3 + -1T = 0

Solving
3 + -1T = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1T = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1T = 0 + -3
-1T = 0 + -3

Combine like terms: 0 + -3 = -3
-1T = -3

Divide each side by '-1'.
T = 3

Simplifying
T = 3
Subproblem 2
Set the factor '(1 + T)' equal to zero and attempt to solve:

Simplifying
1 + T = 0

Solving
1 + T = 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 + T = 0 + -1

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

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

Simplifying
T = -1
Solution
T = {3, -1}