12=5t+3t^2

Solution for 12=5t+3t^2 equation:

Simplifying
12 = 5t + 3t2

Solving
12 = 5t + 3t2

Solving for variable 't'.

Reorder the terms:
12 + -5t + -3t2 = 5t + -5t + 3t2 + -3t2

Combine like terms: 5t + -5t = 0
12 + -5t + -3t2 = 0 + 3t2 + -3t2
12 + -5t + -3t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
12 + -5t + -3t2 = 0

Factor a trinomial.
(4 + -3t)(3 + t) = 0

Subproblem 1
Set the factor '(4 + -3t)' equal to zero and attempt to solve:

Simplifying
4 + -3t = 0

Solving
4 + -3t = 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 + -3t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3t = 0 + -4
-3t = 0 + -4

Combine like terms: 0 + -4 = -4
-3t = -4

Divide each side by '-3'.
t = 1.333333333

Simplifying
t = 1.333333333
Subproblem 2
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 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 + t = 0 + -3

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

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

Simplifying
t = -3
Solution
t = {1.333333333, -3}