9t^2+2t=5t^2

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

Simplifying
9t2 + 2t = 5t2

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

Solving
2t + 9t2 = 5t2

Solving for variable 't'.

Combine like terms: 9t2 + -5t2 = 4t2
2t + 4t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
2t + 4t2 = 0

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

Ignore the factor 2.
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 + 2t)' equal to zero and attempt to solve:

Simplifying
1 + 2t = 0

Solving
1 + 2t = 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 + 2t = 0 + -1

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

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

Divide each side by '2'.
t = -0.5

Simplifying
t = -0.5
Solution
t = {0, -0.5}