6t+45=3t^2

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

Simplifying
6t + 45 = 3t2

Reorder the terms:
45 + 6t = 3t2

Solving
45 + 6t = 3t2

Solving for variable 't'.

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((5 + -1t)(3 + t)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 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 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
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 = {5, -3}