3t^2+9+16t-16-12=0

Solution for 3t^2+9+16t-16-12=0 equation:

Simplifying
3t2 + 9 + 16t + -16 + -12 = 0

Reorder the terms:
9 + -16 + -12 + 16t + 3t2 = 0

Combine like terms: 9 + -16 = -7
-7 + -12 + 16t + 3t2 = 0

Combine like terms: -7 + -12 = -19
-19 + 16t + 3t2 = 0

Solving
-19 + 16t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-19 + -3t)(1 + -1t) = 0

Subproblem 1
Set the factor '(-19 + -3t)' equal to zero and attempt to solve:

Simplifying
-19 + -3t = 0

Solving
-19 + -3t = 0

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

Add '19' to each side of the equation.
-19 + 19 + -3t = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -3t = 0 + 19
-3t = 0 + 19

Combine like terms: 0 + 19 = 19
-3t = 19

Divide each side by '-3'.
t = -6.333333333

Simplifying
t = -6.333333333
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 = {-6.333333333, 1}