45=3t^2+6t

Solution for 45=3t^2+6t equation:

Simplifying
45 = 3t2 + 6t

Reorder the terms:
45 = 6t + 3t2

Solving
45 = 6t + 3t2

Solving for variable 't'.

Reorder the terms:
45 + -6t + -3t2 = 6t + -6t + 3t2 + -3t2

Combine like terms: 6t + -6t = 0
45 + -6t + -3t2 = 0 + 3t2 + -3t2
45 + -6t + -3t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
45 + -6t + -3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + -2t + -1t2) = 0

Factor a trinomial.
3((3 + -1t)(5 + t)) = 0

Ignore the factor 3.
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 '(5 + t)' equal to zero and attempt to solve:

Simplifying
5 + t = 0

Solving
5 + t = 0

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

Add '-5' to each side of the equation.
5 + -5 + t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + t = 0 + -5
t = 0 + -5

Combine like terms: 0 + -5 = -5
t = -5

Simplifying
t = -5
Solution
t = {3, -5}