3t^2=9t-6

Solution for 3t^2=9t-6 equation:

Simplifying
3t2 = 9t + -6

Reorder the terms:
3t2 = -6 + 9t

Solving
3t2 = -6 + 9t

Solving for variable 't'.

Reorder the terms:
6 + -9t + 3t2 = -6 + 9t + 6 + -9t

Reorder the terms:
6 + -9t + 3t2 = -6 + 6 + 9t + -9t

Combine like terms: -6 + 6 = 0
6 + -9t + 3t2 = 0 + 9t + -9t
6 + -9t + 3t2 = 9t + -9t

Combine like terms: 9t + -9t = 0
6 + -9t + 3t2 = 0

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

Factor a trinomial.
3((1 + -1t)(2 + -1t)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {1, 2}