9t^2+2t=5t

Solution for 9t^2+2t=5t equation:

Simplifying
9t2 + 2t = 5t

Reorder the terms:
2t + 9t2 = 5t

Solving
2t + 9t2 = 5t

Solving for variable 't'.

Reorder the terms:
2t + -5t + 9t2 = 5t + -5t

Combine like terms: 2t + -5t = -3t
-3t + 9t2 = 5t + -5t

Combine like terms: 5t + -5t = 0
-3t + 9t2 = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(-1 + 3t)' equal to zero and attempt to solve:

Simplifying
-1 + 3t = 0

Solving
-1 + 3t = 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 + 3t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 3t = 0 + 1
3t = 0 + 1

Combine like terms: 0 + 1 = 1
3t = 1

Divide each side by '3'.
t = 0.3333333333

Simplifying
t = 0.3333333333
Solution
t = {0, 0.3333333333}