12t-45+t^2=0

Solution for 12t-45+t^2=0 equation:

Simplifying
12t + -45 + t2 = 0

Reorder the terms:
-45 + 12t + t2 = 0

Solving
-45 + 12t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-15 + -1t)(3 + -1t) = 0

Subproblem 1
Set the factor '(-15 + -1t)' equal to zero and attempt to solve:

Simplifying
-15 + -1t = 0

Solving
-15 + -1t = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1t = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1t = 0 + 15
-1t = 0 + 15

Combine like terms: 0 + 15 = 15
-1t = 15

Divide each side by '-1'.
t = -15

Simplifying
t = -15
Subproblem 2
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
Solution
t = {-15, 3}