9T^2+12T-5=0

Solution for 9T^2+12T-5=0 equation:

Simplifying
9T2 + 12T + -5 = 0

Reorder the terms:
-5 + 12T + 9T2 = 0

Solving
-5 + 12T + 9T2 = 0

Solving for variable 'T'.

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

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

Simplifying
-5 + -3T = 0

Solving
-5 + -3T = 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 + -3T = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3T = 0 + 5
-3T = 0 + 5

Combine like terms: 0 + 5 = 5
-3T = 5

Divide each side by '-3'.
T = -1.666666667

Simplifying
T = -1.666666667
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 = {-1.666666667, 0.3333333333}